+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0120_identity1 :: Cube -> Bool
+prop_c0120_identity1 cube =
+ c t0 0 1 2 0 ~= (c t0 0 0 2 1 + c t3 0 0 1 2) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0210_identity1 :: Cube -> Bool
+prop_c0210_identity1 cube =
+ c t0 0 2 1 0 ~= (c t0 0 1 1 1 + c t3 0 1 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0300_identity1 :: Cube -> Bool
+prop_c0300_identity1 cube =
+ c t0 0 3 0 0 ~= (c t0 0 2 0 1 + c t3 0 2 1 0) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1110_identity :: Cube -> Bool
+prop_c1110_identity cube =
+ c t0 1 1 1 0 ~= (c t0 1 0 1 1 + c t3 1 0 1 1) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c1200_identity1 :: Cube -> Bool
+prop_c1200_identity1 cube =
+ c t0 1 2 0 0 ~= (c t0 1 1 0 1 + c t3 1 1 1 0) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+
+
+-- | Given in Sorokina and Zeilfelder, p. 79. Note that the third and
+-- fourth indices of c-t3 have been switched. This is because we
+-- store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share <v0,v1,v2> and v3,v3-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c2100_identity1 :: Cube -> Bool
+prop_c2100_identity1 cube =
+ c t0 2 1 0 0 ~= (c t0 2 0 0 1 + c t3 2 0 1 0) / 2
+ where
+ t0 = tetrahedron0 cube
+ t3 = tetrahedron3 cube
+