+-- | Given in Sorokina and Zeilfelder, p. 78.
+prop_cijk1_identity :: Cube -> Bool
+prop_cijk1_identity cube =
+ and [ c t0' i j k 1 ~= (c t1' (i+1) j k 0) * ((b0 t0') (v3 t1')) +
+ (c t1' i (j+1) k 0) * ((b1 t0') (v3 t1')) +
+ (c t1' i j (k+1) 0) * ((b2 t0') (v3 t1')) +
+ (c t1' i j k 1) * ((b3 t0') (v3 t1')) | i <- [0..2],
+ j <- [0..2],
+ k <- [0..2],
+ i + j + k == 2]
+ where
+ t0 = tetrahedron0 (face0 cube)
+ t1 = tetrahedron1 (face0 cube)
+ t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
+ t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
+