From e56404d150410d323a5cc452f7c91e768122a3eb Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Tue, 29 Oct 2024 13:56:30 -0700
Subject: [PATCH 01/13] update: autodetect max int

---
 .../made/tools/build/interface/builders.py    | 47 +++++++++++++++----
 1 file changed, 39 insertions(+), 8 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index f544b581..9fc2e8c9 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -270,36 +270,67 @@ class CommensurateLatticeTwistedInterfaceBuilder(BaseBuilder):
     def _generate(self, configuration: _ConfigurationType) -> List[_GeneratedItemType]:
         film = configuration.film
         # substrate = configuration.substrate
-        max_search = self.build_parameters.max_repetition_int
         a = film.lattice.vector_arrays[0][:2]
         b = film.lattice.vector_arrays[1][:2]
+        max_int = self.__determine_max_int(a, b, configuration.twist_angle)
         commensurate_lattice_pairs = self.__generate_commensurate_lattices(
-            configuration, a, b, max_search, configuration.twist_angle
+            configuration, a, b, max_int, configuration.twist_angle
         )
         return commensurate_lattice_pairs
 
+    def __determine_max_int(self, a: List[float], b: List[float], target_angle: float) -> int:
+        """
+        Determine the maximum integer for the transformation matrices based on the target angle.
+
+        Args:
+            a (List[float]): The a lattice vector.
+            b (List[float]): The b lattice vector.
+            target_angle (float): The target twist angle, in degrees.
+
+        Returns:
+            int: The maximum integer for the transformation matrices.
+        """
+        # Compute the average length of the in-plane lattice vectors
+        length_a = np.linalg.norm(a)
+        length_b = np.linalg.norm(b)
+        average_length = (length_a + length_b) / 2
+
+        # Convert the target angle to radians
+        theta_rad = np.radians(target_angle)
+
+        # Predict the necessary maximum integer for the transformation matrices
+        if theta_rad == 0:
+            max_int = self.build_parameters.max_repetition_int
+        else:
+            max_int = int(np.ceil(average_length / theta_rad))
+
+        # Optional: Limit max_int to a predefined maximum
+        max_int = min(max_int, self.build_parameters.max_repetition_int)
+        return max_int
+
     def __generate_commensurate_lattices(
         self,
         configuration: TwistedInterfaceConfiguration,
         a: List[float],
         b: List[float],
-        max_search: int = 10,
+        max_int: int,
         target_angle: float = 0.0,
     ) -> List[CommensurateLatticePair]:
         """
-        Generate all commensurate lattices for a given search range and filter by closeness to target angle.
+        Generate all commensurate lattices for a given target angle and filter by closeness to target angle.
 
         Args:
             configuration (TwistedInterfaceConfiguration): The configuration for the twisted interface.
             a (List[float]): The a lattice vector.
             b (List[float]): The b lattice vector.
-            max_search (int): The maximum search range.
-            target_angle (float): The target angle, in degrees.
+            max_int (int): The maximum integer for the transformation matrices.
+            target_angle (float): The target twist angle, in degrees.
 
         Returns:
             List[CommensurateLatticePair]: The list of commensurate lattice pairs
         """
-        matrices = create_2d_supercell_matrices(max_search)
+        # Generate the supercell matrices using the calculated max_int
+        matrices = create_2d_supercell_matrices(max_int)
         matrix_ab = np.array([a, b])
         matrix_ab_inverse = np.linalg.inv(matrix_ab)
 
@@ -342,7 +373,7 @@ def _post_process(
             new_film = translate_by_vector(
                 new_film, [0, 0, item.configuration.distance_z], use_cartesian_coordinates=True
             )
-            interface = merge_materials([new_substrate, new_film])
+            interface = merge_materials([new_substrate, new_film], merge_dangerously=True)
             interface.metadata["actual_twist_angle"] = item.angle
             interfaces.append(interface)
         return interfaces

From 43f116beabbf5cbb252796f00a0714d8dd46639e Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Wed, 30 Oct 2024 11:13:21 -0700
Subject: [PATCH 02/13] chore: prune comments

---
 src/py/mat3ra/made/tools/build/interface/builders.py | 7 +------
 1 file changed, 1 insertion(+), 6 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 9fc2e8c9..3f362718 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -290,22 +290,17 @@ def __determine_max_int(self, a: List[float], b: List[float], target_angle: floa
         Returns:
             int: The maximum integer for the transformation matrices.
         """
-        # Compute the average length of the in-plane lattice vectors
         length_a = np.linalg.norm(a)
         length_b = np.linalg.norm(b)
         average_length = (length_a + length_b) / 2
-
-        # Convert the target angle to radians
         theta_rad = np.radians(target_angle)
 
-        # Predict the necessary maximum integer for the transformation matrices
         if theta_rad == 0:
             max_int = self.build_parameters.max_repetition_int
         else:
             max_int = int(np.ceil(average_length / theta_rad))
 
-        # Optional: Limit max_int to a predefined maximum
-        max_int = min(max_int, self.build_parameters.max_repetition_int)
+        max_int = max(max_int, self.build_parameters.max_repetition_int)
         return max_int
 
     def __generate_commensurate_lattices(

From a498c607e6e5e7a654cba142430eb4cd6ea0aea5 Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Wed, 30 Oct 2024 13:55:53 -0700
Subject: [PATCH 03/13] update: rerun with higher max int if not found

---
 .../made/tools/build/interface/builders.py    | 21 +++++++++++--------
 1 file changed, 12 insertions(+), 9 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 3f362718..84110702 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -252,13 +252,14 @@ class CommensurateLatticeTwistedInterfaceBuilderParameters(BaseModel):
     Parameters for the commensurate lattice interface builder.
 
     Args:
-        max_repetition_int (int): The maximum search range for commensurate lattices.
+        max_repetition_int (Optional[int]): The maximum integer for the transformation matrices. If not provided, it
+            will be determined based on the target angle and the lattice vectors automatically.
         angle_tolerance (float): The tolerance for the angle between the commensurate lattices
             and the target angle, in degrees.
         return_first_match (bool): Whether to return the first match or all matches.
     """
 
-    max_repetition_int: int = 10
+    max_repetition_int: Optional[int] = None
     angle_tolerance: float = 0.1
     return_first_match: bool = False
 
@@ -272,10 +273,14 @@ def _generate(self, configuration: _ConfigurationType) -> List[_GeneratedItemTyp
         # substrate = configuration.substrate
         a = film.lattice.vector_arrays[0][:2]
         b = film.lattice.vector_arrays[1][:2]
-        max_int = self.__determine_max_int(a, b, configuration.twist_angle)
-        commensurate_lattice_pairs = self.__generate_commensurate_lattices(
-            configuration, a, b, max_int, configuration.twist_angle
-        )
+        max_int = self.build_parameters.max_repetition_int or self.__determine_max_int(a, b, configuration.twist_angle)
+        commensurate_lattice_pairs: List[CommensurateLatticePair] = []
+        while not commensurate_lattice_pairs:
+            commensurate_lattice_pairs = self.__generate_commensurate_lattices(
+                configuration, a, b, max_int, configuration.twist_angle
+            )
+            max_int += 1
+
         return commensurate_lattice_pairs
 
     def __determine_max_int(self, a: List[float], b: List[float], target_angle: float) -> int:
@@ -296,11 +301,9 @@ def __determine_max_int(self, a: List[float], b: List[float], target_angle: floa
         theta_rad = np.radians(target_angle)
 
         if theta_rad == 0:
-            max_int = self.build_parameters.max_repetition_int
+            max_int = 1
         else:
             max_int = int(np.ceil(average_length / theta_rad))
-
-        max_int = max(max_int, self.build_parameters.max_repetition_int)
         return max_int
 
     def __generate_commensurate_lattices(

From 4428963174a53426cde58ca941791afd959f1568 Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Wed, 30 Oct 2024 15:34:42 -0700
Subject: [PATCH 04/13] update: adjuste name for twisted interfaces

---
 src/py/mat3ra/made/tools/build/interface/builders.py | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 84110702..f4fba72a 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -243,7 +243,7 @@ def _generate(self, configuration: _ConfigurationType) -> List[Material]:
     def _update_material_name(
         self, material: Material, configuration: NanoRibbonTwistedInterfaceConfiguration
     ) -> Material:
-        material.name = f"Twisted Nanoribbon Interface ({configuration.twist_angle:.2f}°)"
+        material.name = f"Twisted Nanoribbon Interface ({configuration.twist_angle:.2f} degrees)"
         return material
 
 
@@ -383,3 +383,9 @@ def _update_material_metadata(self, material, configuration) -> Material:
                 "actual_twist_angle"
             ]
         return updated_material
+
+    def _update_material_name(
+        self, material: Material, configuration: NanoRibbonTwistedInterfaceConfiguration
+    ) -> Material:
+        material.name = f"Twisted Bilayer Interface ({configuration.actual_twist_angle:.2f} degrees)"
+        return material

From da73c3ae9fec4b6592e464892635c0d46352a842 Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Wed, 30 Oct 2024 15:39:43 -0700
Subject: [PATCH 05/13] chore: remove a mistake

---
 src/py/mat3ra/made/tools/build/interface/builders.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index f4fba72a..16dec959 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -387,5 +387,5 @@ def _update_material_metadata(self, material, configuration) -> Material:
     def _update_material_name(
         self, material: Material, configuration: NanoRibbonTwistedInterfaceConfiguration
     ) -> Material:
-        material.name = f"Twisted Bilayer Interface ({configuration.actual_twist_angle:.2f} degrees)"
+        material.name = f"Twisted Bilayer Interface ({material.metadata['actual_twist_angle']:.2f} degrees)"
         return material

From cee4a64a469edf60175e4ca31bb4b06fc2af3dcf Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Thu, 31 Oct 2024 12:18:57 -0700
Subject: [PATCH 06/13] update: add vacuum to twisted interface

---
 src/py/mat3ra/made/tools/build/interface/builders.py      | 3 +++
 src/py/mat3ra/made/tools/build/interface/configuration.py | 1 +
 2 files changed, 4 insertions(+)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 16dec959..14888bc5 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -15,6 +15,7 @@
     rotate,
     translate_by_vector,
     add_vacuum_sides,
+    add_vacuum,
 )
 from ...analyze import get_chemical_formula
 from ...convert import to_ase, from_ase, to_pymatgen, PymatgenInterface, ASEAtoms
@@ -373,6 +374,8 @@ def _post_process(
             )
             interface = merge_materials([new_substrate, new_film], merge_dangerously=True)
             interface.metadata["actual_twist_angle"] = item.angle
+            if item.configuration.vacuum != 0:
+                interface = add_vacuum(interface, item.configuration.vacuum)
             interfaces.append(interface)
         return interfaces
 
diff --git a/src/py/mat3ra/made/tools/build/interface/configuration.py b/src/py/mat3ra/made/tools/build/interface/configuration.py
index 5269c7aa..9f863566 100644
--- a/src/py/mat3ra/made/tools/build/interface/configuration.py
+++ b/src/py/mat3ra/made/tools/build/interface/configuration.py
@@ -40,6 +40,7 @@ class TwistedInterfaceConfiguration(BaseConfiguration):
     substrate: Optional[Material] = None
     twist_angle: float = 0.0
     distance_z: float = 3.0
+    vacuum: float = 0.0
 
     @property
     def _json(self):

From e99cb5d091b95fe9712d95075067758feb6c69fa Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Fri, 1 Nov 2024 20:57:37 -0700
Subject: [PATCH 07/13] wip: tabulate angles for hex

---
 .../made/tools/build/interface/builders.py    | 13 +++++-
 .../made/tools/build/interface/enums.py       | 45 +++++++++++++++++++
 2 files changed, 56 insertions(+), 2 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 14888bc5..b88341af 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -274,7 +274,7 @@ def _generate(self, configuration: _ConfigurationType) -> List[_GeneratedItemTyp
         # substrate = configuration.substrate
         a = film.lattice.vector_arrays[0][:2]
         b = film.lattice.vector_arrays[1][:2]
-        max_int = self.build_parameters.max_repetition_int or self.__determine_max_int(a, b, configuration.twist_angle)
+        max_int = self.build_parameters.max_repetition_int or self.__determine_max_int(film, configuration.twist_angle)
         commensurate_lattice_pairs: List[CommensurateLatticePair] = []
         while not commensurate_lattice_pairs:
             commensurate_lattice_pairs = self.__generate_commensurate_lattices(
@@ -284,7 +284,7 @@ def _generate(self, configuration: _ConfigurationType) -> List[_GeneratedItemTyp
 
         return commensurate_lattice_pairs
 
-    def __determine_max_int(self, a: List[float], b: List[float], target_angle: float) -> int:
+    def __determine_max_int(self, film, target_angle: float) -> int:
         """
         Determine the maximum integer for the transformation matrices based on the target angle.
 
@@ -296,13 +296,22 @@ def __determine_max_int(self, a: List[float], b: List[float], target_angle: floa
         Returns:
             int: The maximum integer for the transformation matrices.
         """
+        a = film.lattice.vector_arrays[0][:2]
+        b = film.lattice.vector_arrays[1][:2]
         length_a = np.linalg.norm(a)
         length_b = np.linalg.norm(b)
         average_length = (length_a + length_b) / 2
         theta_rad = np.radians(target_angle)
 
+        # Factor in both the lattice length and twist angle, ensuring a minimum of 1 for very small angles
         if theta_rad == 0:
             max_int = 1
+        if film.lattice.type == "HEX":
+            from .enums import angle_to_lmpq
+
+            closest_match = min(angle_to_lmpq, key=lambda x: abs(x[0] - target_angle))
+            l, m, p, q = closest_match[1]  # type: ignore
+            max_int = max(l, m, p, q)
         else:
             max_int = int(np.ceil(average_length / theta_rad))
         return max_int
diff --git a/src/py/mat3ra/made/tools/build/interface/enums.py b/src/py/mat3ra/made/tools/build/interface/enums.py
index 364d19b2..4e209059 100644
--- a/src/py/mat3ra/made/tools/build/interface/enums.py
+++ b/src/py/mat3ra/made/tools/build/interface/enums.py
@@ -10,3 +10,48 @@ class StrainModes(str, Enum):
 class SupercellTypes(str, Enum):
     hexagonal = "hexagonal"
     orthogonal = "orthogonal"
+
+
+angle_to_lmpq = [
+    (60.0, [0, 1, -1, 1]),
+    (21.7867892983, [1, 2, -2, 3]),
+    (13.1735511073, [2, 3, -3, 5]),
+    (9.4300079079, [3, 4, -4, 7]),
+    (7.34099301663, [4, 5, -5, 9]),
+    (6.00898319777, [5, 6, -6, 11]),
+    (5.08584780812, [6, 7, -7, 13]),
+    (4.40845500794, [7, 8, -8, 15]),
+    (3.89023816901, [8, 9, -9, 17]),
+    (3.48100608947, [9, 10, -10, 19]),
+    (3.14965742639, [10, 11, -11, 21]),
+    (2.87589463363, [11, 12, -12, 23]),
+    (2.64590838119, [12, 13, -13, 25]),
+    (2.44997727662, [13, 14, -14, 27]),
+    (2.28105960973, [14, 15, -15, 29]),
+    (2.1339296666, [15, 16, -16, 31]),
+    (2.00462783069, [16, 17, -17, 33]),
+    (1.89009907347, [17, 18, -18, 35]),
+    (1.78794861038, [18, 19, -19, 37]),
+    (1.69627269352, [19, 20, -20, 39]),
+    (1.61353890116, [20, 21, -21, 41]),
+    (1.53849981837, [21, 22, -22, 43]),
+    (1.47012972578, [22, 23, -23, 45]),
+    (1.40757744635, [23, 24, -24, 47]),
+    (1.35013073557, [24, 25, -25, 49]),
+    (1.29718904759, [25, 26, -26, 51]),
+    (1.24824246553, [26, 27, -27, 53]),
+    (1.20285522748, [27, 28, -28, 55]),
+    (1.16065271985, [28, 29, -29, 57]),
+    (1.12131111538, [29, 30, -30, 59]),
+    (1.08454904916, [30, 31, -31, 61]),
+    (1.05012087979, [31, 32, -32, 63]),
+    (1.01781119445, [32, 33, -33, 65]),
+    (0.987430297814, [33, 34, -34, 67]),
+    (0.958810485525, [34, 35, -35, 69]),
+    (0.931802947264, [35, 36, -36, 71]),
+    (0.906275178895, [36, 37, -37, 73]),
+    (0.882108808579, [37, 38, -38, 75]),
+    (0.859197761631, [38, 39, -39, 77]),
+    (0.8374467041, [39, 40, -40, 79]),
+    (0.816769716893, [40, 41, -41, 81]),
+]

From 3ab3e7901a1de0b3447edf338a2fbe3e1d074fa0 Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Mon, 4 Nov 2024 10:53:53 -0800
Subject: [PATCH 08/13] chore: small adjustments and renames

---
 .../mat3ra/made/tools/build/interface/builders.py | 15 ++++++++-------
 src/py/mat3ra/made/tools/build/interface/enums.py |  3 ++-
 2 files changed, 10 insertions(+), 8 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index b88341af..0177cc74 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -274,9 +274,11 @@ def _generate(self, configuration: _ConfigurationType) -> List[_GeneratedItemTyp
         # substrate = configuration.substrate
         a = film.lattice.vector_arrays[0][:2]
         b = film.lattice.vector_arrays[1][:2]
-        max_int = self.build_parameters.max_repetition_int or self.__determine_max_int(film, configuration.twist_angle)
+        max_int = self.build_parameters.max_repetition_int or self.__get_initial_guess_for_max_int(
+            film, configuration.twist_angle
+        )
         commensurate_lattice_pairs: List[CommensurateLatticePair] = []
-        while not commensurate_lattice_pairs:
+        while not commensurate_lattice_pairs and max_int < 42:
             commensurate_lattice_pairs = self.__generate_commensurate_lattices(
                 configuration, a, b, max_int, configuration.twist_angle
             )
@@ -284,7 +286,7 @@ def _generate(self, configuration: _ConfigurationType) -> List[_GeneratedItemTyp
 
         return commensurate_lattice_pairs
 
-    def __determine_max_int(self, film, target_angle: float) -> int:
+    def __get_initial_guess_for_max_int(self, film, target_angle: float) -> int:
         """
         Determine the maximum integer for the transformation matrices based on the target angle.
 
@@ -307,11 +309,10 @@ def __determine_max_int(self, film, target_angle: float) -> int:
         if theta_rad == 0:
             max_int = 1
         if film.lattice.type == "HEX":
-            from .enums import angle_to_lmpq
+            from .enums import angle_to_lmpq_hex
 
-            closest_match = min(angle_to_lmpq, key=lambda x: abs(x[0] - target_angle))
-            l, m, p, q = closest_match[1]  # type: ignore
-            max_int = max(l, m, p, q)
+            closest_match = min(angle_to_lmpq_hex, key=lambda x: abs(x[0] - target_angle))
+            max_int = max(closest_match[1])
         else:
             max_int = int(np.ceil(average_length / theta_rad))
         return max_int
diff --git a/src/py/mat3ra/made/tools/build/interface/enums.py b/src/py/mat3ra/made/tools/build/interface/enums.py
index 4e209059..e77df631 100644
--- a/src/py/mat3ra/made/tools/build/interface/enums.py
+++ b/src/py/mat3ra/made/tools/build/interface/enums.py
@@ -12,7 +12,8 @@ class SupercellTypes(str, Enum):
     orthogonal = "orthogonal"
 
 
-angle_to_lmpq = [
+# Tabulation from https://github.com/qtm-iisc/Twister/blob/474156a2a59f2b9d59350b32de56864a9496f848/examples/Homobilayer_hex/hex.table
+angle_to_lmpq_hex = [
     (60.0, [0, 1, -1, 1]),
     (21.7867892983, [1, 2, -2, 3]),
     (13.1735511073, [2, 3, -3, 5]),

From 5f88ce0f0aa96fe8063fa01e783f1279438004aa Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Tue, 5 Nov 2024 13:32:40 -0800
Subject: [PATCH 09/13] update: renames and remove unclear

---
 .../made/tools/build/interface/builders.py    | 43 ++++++++-----------
 .../made/tools/build/interface/enums.py       |  2 +-
 2 files changed, 19 insertions(+), 26 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 0177cc74..4d96f081 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -29,7 +29,7 @@
     ConvertGeneratedItemsPymatgenStructureMixin,
 )
 
-from .enums import StrainModes
+from .enums import StrainModes, angle_to_supercell_matrix_values_for_hex
 from .configuration import (
     InterfaceConfiguration,
     NanoRibbonTwistedInterfaceConfiguration,
@@ -253,14 +253,16 @@ class CommensurateLatticeTwistedInterfaceBuilderParameters(BaseModel):
     Parameters for the commensurate lattice interface builder.
 
     Args:
-        max_repetition_int (Optional[int]): The maximum integer for the transformation matrices. If not provided, it
-            will be determined based on the target angle and the lattice vectors automatically.
+        max_supercell_matrix_int (Optional[int]): The maximum integer for the transformation matrices.
+            If not provided, it will be determined based on the target angle and the lattice vectors automatically.
+        limit_max_int (Optional[int]): The limit for the maximum integer for the transformation matrices when searching
         angle_tolerance (float): The tolerance for the angle between the commensurate lattices
             and the target angle, in degrees.
         return_first_match (bool): Whether to return the first match or all matches.
     """
 
-    max_repetition_int: Optional[int] = None
+    max_supercell_matrix_int: Optional[int] = None
+    limit_max_int: Optional[int] = 42
     angle_tolerance: float = 0.1
     return_first_match: bool = False
 
@@ -274,11 +276,12 @@ def _generate(self, configuration: _ConfigurationType) -> List[_GeneratedItemTyp
         # substrate = configuration.substrate
         a = film.lattice.vector_arrays[0][:2]
         b = film.lattice.vector_arrays[1][:2]
-        max_int = self.build_parameters.max_repetition_int or self.__get_initial_guess_for_max_int(
+        max_int = self.build_parameters.max_supercell_matrix_int or self.__get_initial_guess_for_max_int(
             film, configuration.twist_angle
         )
         commensurate_lattice_pairs: List[CommensurateLatticePair] = []
-        while not commensurate_lattice_pairs and max_int < 42:
+        while not commensurate_lattice_pairs and max_int < self.build_parameters.limit_max_int:
+            print(f"Trying max_int = {max_int}")
             commensurate_lattice_pairs = self.__generate_commensurate_lattices(
                 configuration, a, b, max_int, configuration.twist_angle
             )
@@ -298,23 +301,13 @@ def __get_initial_guess_for_max_int(self, film, target_angle: float) -> int:
         Returns:
             int: The maximum integer for the transformation matrices.
         """
-        a = film.lattice.vector_arrays[0][:2]
-        b = film.lattice.vector_arrays[1][:2]
-        length_a = np.linalg.norm(a)
-        length_b = np.linalg.norm(b)
-        average_length = (length_a + length_b) / 2
-        theta_rad = np.radians(target_angle)
-
-        # Factor in both the lattice length and twist angle, ensuring a minimum of 1 for very small angles
-        if theta_rad == 0:
+        if np.isclose(target_angle, 0.0, atol=0.01):
             max_int = 1
         if film.lattice.type == "HEX":
-            from .enums import angle_to_lmpq_hex
-
-            closest_match = min(angle_to_lmpq_hex, key=lambda x: abs(x[0] - target_angle))
-            max_int = max(closest_match[1])
-        else:
-            max_int = int(np.ceil(average_length / theta_rad))
+            tabulated_matrix_match_for_given_angle = min(
+                angle_to_supercell_matrix_values_for_hex, key=lambda x: abs(x[0] - target_angle)
+            )
+            max_int = max(tabulated_matrix_match_for_given_angle[1])
         return max_int
 
     def __generate_commensurate_lattices(
@@ -322,7 +315,7 @@ def __generate_commensurate_lattices(
         configuration: TwistedInterfaceConfiguration,
         a: List[float],
         b: List[float],
-        max_int: int,
+        max_supercell_matrix_element_int: int,
         target_angle: float = 0.0,
     ) -> List[CommensurateLatticePair]:
         """
@@ -332,14 +325,14 @@ def __generate_commensurate_lattices(
             configuration (TwistedInterfaceConfiguration): The configuration for the twisted interface.
             a (List[float]): The a lattice vector.
             b (List[float]): The b lattice vector.
-            max_int (int): The maximum integer for the transformation matrices.
+            max_supercell_matrix_element_int (int): The maximum integer for the transformation matrices.
             target_angle (float): The target twist angle, in degrees.
 
         Returns:
             List[CommensurateLatticePair]: The list of commensurate lattice pairs
         """
-        # Generate the supercell matrices using the calculated max_int
-        matrices = create_2d_supercell_matrices(max_int)
+        # Generate the supercell matrices using the calculated max_supercell_matrix_element_int
+        matrices = create_2d_supercell_matrices(max_supercell_matrix_element_int)
         matrix_ab = np.array([a, b])
         matrix_ab_inverse = np.linalg.inv(matrix_ab)
 
diff --git a/src/py/mat3ra/made/tools/build/interface/enums.py b/src/py/mat3ra/made/tools/build/interface/enums.py
index e77df631..2f62e46f 100644
--- a/src/py/mat3ra/made/tools/build/interface/enums.py
+++ b/src/py/mat3ra/made/tools/build/interface/enums.py
@@ -13,7 +13,7 @@ class SupercellTypes(str, Enum):
 
 
 # Tabulation from https://github.com/qtm-iisc/Twister/blob/474156a2a59f2b9d59350b32de56864a9496f848/examples/Homobilayer_hex/hex.table
-angle_to_lmpq_hex = [
+angle_to_supercell_matrix_values_for_hex = [
     (60.0, [0, 1, -1, 1]),
     (21.7867892983, [1, 2, -2, 3]),
     (13.1735511073, [2, 3, -3, 5]),

From 357bca33e585f394d6e90c60fe47403c2a457efe Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Tue, 5 Nov 2024 13:37:16 -0800
Subject: [PATCH 10/13] update: simplify

---
 src/py/mat3ra/made/tools/build/interface/builders.py | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 4d96f081..8736e1f3 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -301,14 +301,12 @@ def __get_initial_guess_for_max_int(self, film, target_angle: float) -> int:
         Returns:
             int: The maximum integer for the transformation matrices.
         """
-        if np.isclose(target_angle, 0.0, atol=0.01):
-            max_int = 1
         if film.lattice.type == "HEX":
             tabulated_matrix_match_for_given_angle = min(
                 angle_to_supercell_matrix_values_for_hex, key=lambda x: abs(x[0] - target_angle)
             )
-            max_int = max(tabulated_matrix_match_for_given_angle[1])
-        return max_int
+            return max(tabulated_matrix_match_for_given_angle[1])
+        return 1
 
     def __generate_commensurate_lattices(
         self,

From 69acbd44a3c6fb37e5babdfa40133fb894c89daf Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Tue, 5 Nov 2024 16:16:27 -0800
Subject: [PATCH 11/13] update: add case for 0 degrees

---
 src/py/mat3ra/made/tools/build/interface/enums.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/py/mat3ra/made/tools/build/interface/enums.py b/src/py/mat3ra/made/tools/build/interface/enums.py
index 2f62e46f..96d149cc 100644
--- a/src/py/mat3ra/made/tools/build/interface/enums.py
+++ b/src/py/mat3ra/made/tools/build/interface/enums.py
@@ -55,4 +55,5 @@ class SupercellTypes(str, Enum):
     (0.859197761631, [38, 39, -39, 77]),
     (0.8374467041, [39, 40, -40, 79]),
     (0.816769716893, [40, 41, -41, 81]),
+    (0.0, [1, 0, 0, 1]),
 ]

From 356e51b23a2415e5f8315d534a3853ec3705b8bd Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Tue, 5 Nov 2024 21:16:51 -0800
Subject: [PATCH 12/13] chore: turn angle-matrix into map

---
 .../made/tools/build/interface/builders.py    |  6 +-
 .../made/tools/build/interface/enums.py       | 85 ++++++++++---------
 2 files changed, 46 insertions(+), 45 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 8736e1f3..3f302f14 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -302,10 +302,10 @@ def __get_initial_guess_for_max_int(self, film, target_angle: float) -> int:
             int: The maximum integer for the transformation matrices.
         """
         if film.lattice.type == "HEX":
-            tabulated_matrix_match_for_given_angle = min(
-                angle_to_supercell_matrix_values_for_hex, key=lambda x: abs(x[0] - target_angle)
+            xy_supercell_matrix_for_closest_angle = min(
+                angle_to_supercell_matrix_values_for_hex, key=lambda x: abs(float(x["angle"]) - target_angle)
             )
-            return max(tabulated_matrix_match_for_given_angle[1])
+            return max(**xy_supercell_matrix_for_closest_angle["xy_supercell"])
         return 1
 
     def __generate_commensurate_lattices(
diff --git a/src/py/mat3ra/made/tools/build/interface/enums.py b/src/py/mat3ra/made/tools/build/interface/enums.py
index 96d149cc..d19fe43e 100644
--- a/src/py/mat3ra/made/tools/build/interface/enums.py
+++ b/src/py/mat3ra/made/tools/build/interface/enums.py
@@ -13,47 +13,48 @@ class SupercellTypes(str, Enum):
 
 
 # Tabulation from https://github.com/qtm-iisc/Twister/blob/474156a2a59f2b9d59350b32de56864a9496f848/examples/Homobilayer_hex/hex.table
+# Maps twist angle to supercell matrix values for homo-material hexagonal supercells bilayer
 angle_to_supercell_matrix_values_for_hex = [
-    (60.0, [0, 1, -1, 1]),
-    (21.7867892983, [1, 2, -2, 3]),
-    (13.1735511073, [2, 3, -3, 5]),
-    (9.4300079079, [3, 4, -4, 7]),
-    (7.34099301663, [4, 5, -5, 9]),
-    (6.00898319777, [5, 6, -6, 11]),
-    (5.08584780812, [6, 7, -7, 13]),
-    (4.40845500794, [7, 8, -8, 15]),
-    (3.89023816901, [8, 9, -9, 17]),
-    (3.48100608947, [9, 10, -10, 19]),
-    (3.14965742639, [10, 11, -11, 21]),
-    (2.87589463363, [11, 12, -12, 23]),
-    (2.64590838119, [12, 13, -13, 25]),
-    (2.44997727662, [13, 14, -14, 27]),
-    (2.28105960973, [14, 15, -15, 29]),
-    (2.1339296666, [15, 16, -16, 31]),
-    (2.00462783069, [16, 17, -17, 33]),
-    (1.89009907347, [17, 18, -18, 35]),
-    (1.78794861038, [18, 19, -19, 37]),
-    (1.69627269352, [19, 20, -20, 39]),
-    (1.61353890116, [20, 21, -21, 41]),
-    (1.53849981837, [21, 22, -22, 43]),
-    (1.47012972578, [22, 23, -23, 45]),
-    (1.40757744635, [23, 24, -24, 47]),
-    (1.35013073557, [24, 25, -25, 49]),
-    (1.29718904759, [25, 26, -26, 51]),
-    (1.24824246553, [26, 27, -27, 53]),
-    (1.20285522748, [27, 28, -28, 55]),
-    (1.16065271985, [28, 29, -29, 57]),
-    (1.12131111538, [29, 30, -30, 59]),
-    (1.08454904916, [30, 31, -31, 61]),
-    (1.05012087979, [31, 32, -32, 63]),
-    (1.01781119445, [32, 33, -33, 65]),
-    (0.987430297814, [33, 34, -34, 67]),
-    (0.958810485525, [34, 35, -35, 69]),
-    (0.931802947264, [35, 36, -36, 71]),
-    (0.906275178895, [36, 37, -37, 73]),
-    (0.882108808579, [37, 38, -38, 75]),
-    (0.859197761631, [38, 39, -39, 77]),
-    (0.8374467041, [39, 40, -40, 79]),
-    (0.816769716893, [40, 41, -41, 81]),
-    (0.0, [1, 0, 0, 1]),
+    {"angle": 60.0, "xy_supercell": [[0, 1], [-1, 1]]},
+    {"angle": 21.7867892983, "xy_supercell": [[1, 2], [-2, 3]]},
+    {"angle": 13.1735511073, "xy_supercell": [[2, 3], [-3, 5]]},
+    {"angle": 9.4300079079, "xy_supercell": [[3, 4], [-4, 7]]},
+    {"angle": 7.34099301663, "xy_supercell": [[4, 5], [-5, 9]]},
+    {"angle": 6.00898319777, "xy_supercell": [[5, 6], [-6, 11]]},
+    {"angle": 5.08584780812, "xy_supercell": [[6, 7], [-7, 13]]},
+    {"angle": 4.40845500794, "xy_supercell": [[7, 8], [-8, 15]]},
+    {"angle": 3.89023816901, "xy_supercell": [[8, 9], [-9, 17]]},
+    {"angle": 3.48100608947, "xy_supercell": [[9, 10], [-10, 19]]},
+    {"angle": 3.14965742639, "xy_supercell": [[10, 11], [-11, 21]]},
+    {"angle": 2.87589463363, "xy_supercell": [[11, 12], [-12, 23]]},
+    {"angle": 2.64590838119, "xy_supercell": [[12, 13], [-13, 25]]},
+    {"angle": 2.44997727662, "xy_supercell": [[13, 14], [-14, 27]]},
+    {"angle": 2.28105960973, "xy_supercell": [[14, 15], [-15, 29]]},
+    {"angle": 2.1339296666, "xy_supercell": [[15, 16], [-16, 31]]},
+    {"angle": 2.00462783069, "xy_supercell": [[16, 17], [-17, 33]]},
+    {"angle": 1.89009907347, "xy_supercell": [[17, 18], [-18, 35]]},
+    {"angle": 1.78794861038, "xy_supercell": [[18, 19], [-19, 37]]},
+    {"angle": 1.69627269352, "xy_supercell": [[19, 20], [-20, 39]]},
+    {"angle": 1.61353890116, "xy_supercell": [[20, 21], [-21, 41]]},
+    {"angle": 1.53849981837, "xy_supercell": [[21, 22], [-22, 43]]},
+    {"angle": 1.47012972578, "xy_supercell": [[22, 23], [-23, 45]]},
+    {"angle": 1.40757744635, "xy_supercell": [[23, 24], [-24, 47]]},
+    {"angle": 1.35013073557, "xy_supercell": [[24, 25], [-25, 49]]},
+    {"angle": 1.29718904759, "xy_supercell": [[25, 26], [-26, 51]]},
+    {"angle": 1.24824246553, "xy_supercell": [[26, 27], [-27, 53]]},
+    {"angle": 1.20285522748, "xy_supercell": [[27, 28], [-28, 55]]},
+    {"angle": 1.16065271985, "xy_supercell": [[28, 29], [-29, 57]]},
+    {"angle": 1.12131111538, "xy_supercell": [[29, 30], [-30, 59]]},
+    {"angle": 1.08454904916, "xy_supercell": [[30, 31], [-31, 61]]},
+    {"angle": 1.05012087979, "xy_supercell": [[31, 32], [-32, 63]]},
+    {"angle": 1.01781119445, "xy_supercell": [[32, 33], [-33, 65]]},
+    {"angle": 0.987430297814, "xy_supercell": [[33, 34], [-34, 67]]},
+    {"angle": 0.958810485525, "xy_supercell": [[34, 35], [-35, 69]]},
+    {"angle": 0.931802947264, "xy_supercell": [[35, 36], [-36, 71]]},
+    {"angle": 0.906275178895, "xy_supercell": [[36, 37], [-37, 73]]},
+    {"angle": 0.882108808579, "xy_supercell": [[37, 38], [-38, 75]]},
+    {"angle": 0.859197761631, "xy_supercell": [[38, 39], [-39, 77]]},
+    {"angle": 0.8374467041, "xy_supercell": [[39, 40], [-40, 79]]},
+    {"angle": 0.816769716893, "xy_supercell": [[40, 41], [-41, 81]]},
+    {"angle": 0.0, "xy_supercell": [[1, 0], [0, 1]]},
 ]

From 75ac32169f9f7ed1a44cc0057faeffde45796950 Mon Sep 17 00:00:00 2001
From: VsevolodX <79542055+VsevolodX@users.noreply.github.com>
Date: Tue, 5 Nov 2024 21:26:18 -0800
Subject: [PATCH 13/13] update: fix error

---
 src/py/mat3ra/made/tools/build/interface/builders.py | 6 ++++--
 src/py/mat3ra/made/tools/build/interface/enums.py    | 8 +++++++-
 2 files changed, 11 insertions(+), 3 deletions(-)

diff --git a/src/py/mat3ra/made/tools/build/interface/builders.py b/src/py/mat3ra/made/tools/build/interface/builders.py
index 3f302f14..2c72c1c6 100644
--- a/src/py/mat3ra/made/tools/build/interface/builders.py
+++ b/src/py/mat3ra/made/tools/build/interface/builders.py
@@ -302,10 +302,12 @@ def __get_initial_guess_for_max_int(self, film, target_angle: float) -> int:
             int: The maximum integer for the transformation matrices.
         """
         if film.lattice.type == "HEX":
+            # getting max int of the matrix that has angle closest to target angle
             xy_supercell_matrix_for_closest_angle = min(
-                angle_to_supercell_matrix_values_for_hex, key=lambda x: abs(float(x["angle"]) - target_angle)
+                angle_to_supercell_matrix_values_for_hex, key=lambda x: abs(x["angle"] - target_angle)
             )
-            return max(**xy_supercell_matrix_for_closest_angle["xy_supercell"])
+            # Get maximum absolute value from the supercell matrix values
+            return max(abs(x) for row in xy_supercell_matrix_for_closest_angle["xy_supercell"] for x in row)
         return 1
 
     def __generate_commensurate_lattices(
diff --git a/src/py/mat3ra/made/tools/build/interface/enums.py b/src/py/mat3ra/made/tools/build/interface/enums.py
index d19fe43e..7a776006 100644
--- a/src/py/mat3ra/made/tools/build/interface/enums.py
+++ b/src/py/mat3ra/made/tools/build/interface/enums.py
@@ -1,4 +1,5 @@
 from enum import Enum
+from typing import TypedDict, List
 
 
 class StrainModes(str, Enum):
@@ -12,9 +13,14 @@ class SupercellTypes(str, Enum):
     orthogonal = "orthogonal"
 
 
+class SupercellMatrix(TypedDict):
+    angle: float
+    xy_supercell: List[List[int]]
+
+
 # Tabulation from https://github.com/qtm-iisc/Twister/blob/474156a2a59f2b9d59350b32de56864a9496f848/examples/Homobilayer_hex/hex.table
 # Maps twist angle to supercell matrix values for homo-material hexagonal supercells bilayer
-angle_to_supercell_matrix_values_for_hex = [
+angle_to_supercell_matrix_values_for_hex: List[SupercellMatrix] = [
     {"angle": 60.0, "xy_supercell": [[0, 1], [-1, 1]]},
     {"angle": 21.7867892983, "xy_supercell": [[1, 2], [-2, 3]]},
     {"angle": 13.1735511073, "xy_supercell": [[2, 3], [-3, 5]]},