+-- Face stuff.
+
+-- | The top (in the direction of z) face of the cube.
+top_face :: Cube -> Face.Face
+top_face c = Face.Face v0' v1' v2' v3'
+ where
+ delta = (1/2)*(h c)
+ v0' = (center c) + (delta, -delta, delta)
+ v1' = (center c) + (delta, delta, delta)
+ v2' = (center c) + (-delta, delta, delta)
+ v3' = (center c) + (-delta, -delta, delta)
+
+
+
+-- | The back (in the direction of x) face of the cube.
+back_face :: Cube -> Face.Face
+back_face c = Face.Face v0' v1' v2' v3'
+ where
+ delta = (1/2)*(h c)
+ v0' = (center c) + (delta, -delta, -delta)
+ v1' = (center c) + (delta, delta, -delta)
+ v2' = (center c) + (delta, delta, delta)
+ v3' = (center c) + (delta, -delta, delta)
+
+
+-- The bottom face (in the direction of -z) of the cube.
+down_face :: Cube -> Face.Face
+down_face c = Face.Face v0' v1' v2' v3'
+ where
+ delta = (1/2)*(h c)
+ v0' = (center c) + (-delta, -delta, -delta)
+ v1' = (center c) + (-delta, delta, -delta)
+ v2' = (center c) + (delta, delta, -delta)
+ v3' = (center c) + (delta, -delta, -delta)
+
+
+
+-- | The front (in the direction of -x) face of the cube.
+front_face :: Cube -> Face.Face
+front_face c = Face.Face v0' v1' v2' v3'
+ where
+ delta = (1/2)*(h c)
+ v0' = (center c) + (-delta, -delta, delta)
+ v1' = (center c) + (-delta, delta, delta)
+ v2' = (center c) + (-delta, delta, -delta)
+ v3' = (center c) + (-delta, -delta, -delta)
+
+-- | The left (in the direction of -y) face of the cube.
+left_face :: Cube -> Face.Face
+left_face c = Face.Face v0' v1' v2' v3'
+ where
+ delta = (1/2)*(h c)
+ v0' = (center c) + (delta, -delta, delta)
+ v1' = (center c) + (-delta, -delta, delta)
+ v2' = (center c) + (-delta, -delta, -delta)
+ v3' = (center c) + (delta, -delta, -delta)
+
+
+-- | The right (in the direction of y) face of the cube.
+right_face :: Cube -> Face.Face
+right_face c = Face.Face v0' v1' v2' v3'
+ where
+ delta = (1/2)*(h c)
+ v0' = (center c) + (-delta, delta, delta)
+ v1' = (center c) + (delta, delta, delta)
+ v2' = (center c) + (delta, delta, -delta)
+ v3' = (center c) + (-delta, delta, -delta)
+
+
+tetrahedron0 :: Cube -> Tetrahedron
+tetrahedron0 c =
+ Tetrahedron (Cube.fv c) v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (front_face c)
+ v2' = Face.v0 (front_face c)
+ v3' = Face.v1 (front_face c)
+
+tetrahedron1 :: Cube -> Tetrahedron
+tetrahedron1 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (front_face c)
+ v2' = Face.v1 (front_face c)
+ v3' = Face.v2 (front_face c)
+ fv' = rotate (Cube.fv c) ccwx
+
+tetrahedron2 :: Cube -> Tetrahedron
+tetrahedron2 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (front_face c)
+ v2' = Face.v2 (front_face c)
+ v3' = Face.v3 (front_face c)
+ fv' = rotate (Cube.fv c) (ccwx . ccwx)
+
+tetrahedron3 :: Cube -> Tetrahedron
+tetrahedron3 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (front_face c)
+ v2' = Face.v3 (front_face c)
+ v3' = Face.v0 (front_face c)
+ fv' = rotate (Cube.fv c) cwx
+
+tetrahedron4 :: Cube -> Tetrahedron
+tetrahedron4 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (top_face c)
+ v2' = Face.v0 (top_face c)
+ v3' = Face.v1 (top_face c)
+ fv' = rotate (Cube.fv c) cwy
+
+tetrahedron5 :: Cube -> Tetrahedron
+tetrahedron5 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (top_face c)
+ v2' = Face.v1 (top_face c)
+ v3' = Face.v2 (top_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwz
+
+tetrahedron6 :: Cube -> Tetrahedron
+tetrahedron6 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (top_face c)
+ v2' = Face.v2 (top_face c)
+ v3' = Face.v3 (top_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) (ccwz . ccwz)
+
+tetrahedron7 :: Cube -> Tetrahedron
+tetrahedron7 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (top_face c)
+ v2' = Face.v3 (top_face c)
+ v3' = Face.v0 (top_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwz
+
+tetrahedron8 :: Cube -> Tetrahedron
+tetrahedron8 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v0 (back_face c)
+ v3' = Face.v1 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwy
+
+tetrahedron9 :: Cube -> Tetrahedron
+tetrahedron9 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v1 (back_face c)
+ v3' = Face.v2 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) ccwx
+
+tetrahedron10 :: Cube -> Tetrahedron
+tetrahedron10 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v2 (back_face c)
+ v3' = Face.v3 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) (ccwx . ccwx)
+
+
+tetrahedron11 :: Cube -> Tetrahedron
+tetrahedron11 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v3 (back_face c)
+ v3' = Face.v0 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwx
+
+
+tetrahedron12 :: Cube -> Tetrahedron
+tetrahedron12 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v0 (down_face c)
+ v3' = Face.v1 (down_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwy
+
+
+tetrahedron13 :: Cube -> Tetrahedron
+tetrahedron13 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v1 (down_face c)
+ v3' = Face.v2 (down_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) ccwz
+
+
+tetrahedron14 :: Cube -> Tetrahedron
+tetrahedron14 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v2 (down_face c)
+ v3' = Face.v3 (down_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron13 c)) (ccwz . ccwz)
+