4 -- -- | Given in Sorokina and Zeilfelder, p. 79.
5 -- prop_c0210_identity1 :: Cube -> Bool
6 -- prop_c0210_identity1 cube =
7 -- c t0' 0 2 1 0 ~= (c t0' 0 1 1 1 + c t1' 0 1 1 1) / 2
9 -- t0 = tetrahedron0 (face0 cube)
10 -- t1 = tetrahedron1 (face0 cube)
11 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
12 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
15 -- -- | Given in Sorokina and Zeilfelder, p. 79.
16 -- prop_c0300_identity1 :: Cube -> Bool
17 -- prop_c0300_identity1 cube =
18 -- c t0' 0 3 0 0 ~= (c t0' 0 2 0 1 + c t1' 0 2 0 1) / 2
20 -- t0 = tetrahedron0 (face0 cube)
21 -- t1 = tetrahedron1 (face0 cube)
22 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
23 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
25 -- -- | Given in Sorokina and Zeilfelder, p. 79.
26 -- prop_c1110_identity :: Cube -> Bool
27 -- prop_c1110_identity cube =
28 -- c t0' 1 1 1 0 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
30 -- t0 = tetrahedron0 (face0 cube)
31 -- t1 = tetrahedron1 (face0 cube)
32 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
33 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
36 -- -- | Given in Sorokina and Zeilfelder, p. 79.
37 -- prop_c1200_identity1 :: Cube -> Bool
38 -- prop_c1200_identity1 cube =
39 -- c t0' 1 2 0 0 ~= (c t0' 1 1 0 1 + c t1' 1 1 0 1) / 2
41 -- t0 = tetrahedron0 (face0 cube)
42 -- t1 = tetrahedron1 (face0 cube)
43 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
44 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
47 -- -- | Given in Sorokina and Zeilfelder, p. 79.
48 -- prop_c2100_identity1 :: Cube -> Bool
49 -- prop_c2100_identity1 cube =
50 -- c t0' 2 1 0 0 ~= (c t0' 2 0 0 1 + c t1' 2 0 0 1) / 2
52 -- t0 = tetrahedron0 (face0 cube)
53 -- t1 = tetrahedron1 (face0 cube)
54 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
55 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
58 -- -- | Given in Sorokina and Zeilfelder, p. 79.
59 -- prop_c0102_identity1 :: Cube -> Bool
60 -- prop_c0102_identity1 cube =
61 -- c t0' 0 1 0 2 ~= (c t0' 0 0 1 2 + c t3' 0 0 1 2) / 2
63 -- t0 = tetrahedron0 (face0 cube)
64 -- t3 = tetrahedron3 (face0 cube)
65 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
66 -- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
69 -- -- | Given in Sorokina and Zeilfelder, p. 79.
70 -- prop_c0201_identity1 :: Cube -> Bool
71 -- prop_c0201_identity1 cube =
72 -- c t0' 0 2 0 1 ~= (c t0' 0 1 1 1 + c t3' 0 1 1 1) / 2
74 -- t0 = tetrahedron0 (face0 cube)
75 -- t3 = tetrahedron3 (face0 cube)
76 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
77 -- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
80 -- -- | Given in Sorokina and Zeilfelder, p. 79.
81 -- prop_c0300_identity2 :: Cube -> Bool
82 -- prop_c0300_identity2 cube =
83 -- c t0' 3 0 0 0 ~= (c t0' 0 2 1 0 + c t3' 0 2 1 0) / 2
85 -- t0 = tetrahedron0 (face0 cube)
86 -- t3 = tetrahedron3 (face0 cube)
87 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
88 -- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
90 -- -- | Given in Sorokina and Zeilfelder, p. 79.
91 -- prop_c1101_identity :: Cube -> Bool
92 -- prop_c1101_identity cube =
93 -- c t0' 1 1 0 1 ~= (c t0' 1 1 0 1 + c t3' 1 1 0 1) / 2
95 -- t0 = tetrahedron0 (face0 cube)
96 -- t3 = tetrahedron3 (face0 cube)
97 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
98 -- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
101 -- -- | Given in Sorokina and Zeilfelder, p. 79.
102 -- prop_c1200_identity2 :: Cube -> Bool
103 -- prop_c1200_identity2 cube =
104 -- c t0' 1 1 1 0 ~= (c t0' 1 1 1 0 + c t3' 1 1 1 0) / 2
106 -- t0 = tetrahedron0 (face0 cube)
107 -- t3 = tetrahedron3 (face0 cube)
108 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
109 -- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
112 -- -- | Given in Sorokina and Zeilfelder, p. 79.
113 -- prop_c2100_identity2 :: Cube -> Bool
114 -- prop_c2100_identity2 cube =
115 -- c t0' 2 1 0 0 ~= (c t0' 2 0 1 0 + c t3' 2 0 1 0) / 2
117 -- t0 = tetrahedron0 (face0 cube)
118 -- t3 = tetrahedron3 (face0 cube)
119 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
120 -- t3' = Tetrahedron cube (v3 t3) (v2 t3) (v1 t3) (v0 t3)
123 -- -- | Given in Sorokina and Zeilfelder, p. 79.
124 -- prop_c3000_identity :: Cube -> Bool
125 -- prop_c3000_identity cube =
126 -- c t0' 3 0 0 0 ~= c t0' 2 1 0 0 + c t2' 2 1 0 0 - ((c t0' 2 0 1 0 + c t0' 2 0 0 1)/ 2)
128 -- t0 = tetrahedron0 (face0 cube)
129 -- t2 = tetrahedron2 (face5 cube)
130 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
131 -- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
134 -- -- | Given in Sorokina and Zeilfelder, p. 79.
135 -- prop_c2010_identity :: Cube -> Bool
136 -- prop_c2010_identity cube =
137 -- c t0' 2 0 1 0 ~= c t0' 1 1 1 0 + c t2' 1 1 1 0 - ((c t0' 1 0 2 0 + c t0' 1 0 1 1)/ 2)
139 -- t0 = tetrahedron0 (face0 cube)
140 -- t2 = tetrahedron2 (face5 cube)
141 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
142 -- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
145 -- -- | Given in Sorokina and Zeilfelder, p. 79.
146 -- prop_c2001_identity :: Cube -> Bool
147 -- prop_c2001_identity cube =
148 -- c t0' 2 0 0 1 ~= c t0' 1 1 0 1 + c t2' 1 1 0 1 - ((c t0' 1 0 0 2 + c t0' 1 0 1 1)/ 2)
150 -- t0 = tetrahedron0 (face0 cube)
151 -- t2 = tetrahedron2 (face5 cube)
152 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
153 -- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
155 -- -- | Given in Sorokina and Zeilfelder, p. 79.
156 -- prop_c1020_identity :: Cube -> Bool
157 -- prop_c1020_identity cube =
158 -- c t0' 1 0 2 0 ~= c t0' 0 1 2 0 + c t2' 0 1 2 0 - ((c t0' 0 0 3 0 + c t0' 0 0 2 1)/ 2)
160 -- t0 = tetrahedron0 (face0 cube)
161 -- t2 = tetrahedron2 (face5 cube)
162 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
163 -- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
166 -- -- | Given in Sorokina and Zeilfelder, p. 79.
167 -- prop_c1002_identity :: Cube -> Bool
168 -- prop_c1002_identity cube =
169 -- c t0' 1 0 0 2 ~= c t0' 0 1 0 2 + c t2' 0 1 0 2 - ((c t0' 0 0 0 3 + c t0' 0 0 1 2)/ 2)
171 -- t0 = tetrahedron0 (face0 cube)
172 -- t2 = tetrahedron2 (face5 cube)
173 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
174 -- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
177 -- -- | Given in Sorokina and Zeilfelder, p. 79.
178 -- prop_c1011_identity :: Cube -> Bool
179 -- prop_c1011_identity cube =
180 -- c t0' 1 0 1 1 ~= c t0' 0 1 1 1 + c t2' 0 1 1 1 - ((c t0' 0 0 1 2 + c t0' 0 0 2 1)/ 2)
182 -- t0 = tetrahedron0 (face0 cube)
183 -- t2 = tetrahedron2 (face5 cube)
184 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
185 -- t2' = Tetrahedron cube (v3 t2) (v2 t2) (v1 t2) (v0 t2)
188 -- -- | Given in Sorokina and Zeilfelder, p. 80.
189 -- prop_c0120_identity2 :: Cube -> Bool
190 -- prop_c0120_identity2 cube =
191 -- c t0' 0 1 2 0 ~= (c t0' 1 0 2 0 + c t1' 1 0 2 0) / 2
193 -- t0 = tetrahedron0 (face0 cube)
194 -- t1 = tetrahedron0 (face2 (top cube))
195 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
196 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
199 -- -- | Given in Sorokina and Zeilfelder, p. 80.
200 -- prop_c0102_identity2 :: Cube -> Bool
201 -- prop_c0102_identity2 cube =
202 -- c t0' 0 1 0 2 ~= (c t0' 1 0 0 2 + c t1' 1 0 0 2) / 2
204 -- t0 = tetrahedron0 (face0 cube)
205 -- t1 = tetrahedron0 (face2 (top cube))
206 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
207 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
210 -- -- | Given in Sorokina and Zeilfelder, p. 80.
211 -- prop_c0111_identity :: Cube -> Bool
212 -- prop_c0111_identity cube =
213 -- c t0' 0 1 1 1 ~= (c t0' 1 0 1 1 + c t1' 1 0 1 1) / 2
215 -- t0 = tetrahedron0 (face0 cube)
216 -- t1 = tetrahedron0 (face2 (top cube))
217 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
218 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
221 -- -- | Given in Sorokina and Zeilfelder, p. 80.
222 -- prop_c0210_identity2 :: Cube -> Bool
223 -- prop_c0210_identity2 cube =
224 -- c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t1 1 1 1 0) / 2
226 -- t0 = tetrahedron0 (face0 cube)
227 -- t1 = tetrahedron0 (face2 (top cube))
228 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
229 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
232 -- -- | Given in Sorokina and Zeilfelder, p. 80.
233 -- prop_c0201_identity2 :: Cube -> Bool
234 -- prop_c0201_identity2 cube =
235 -- c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t1 1 1 0 1) / 2
237 -- t0 = tetrahedron0 (face0 cube)
238 -- t1 = tetrahedron0 (face2 (top cube))
239 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
240 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)
243 -- -- | Given in Sorokina and Zeilfelder, p. 80.
244 -- prop_c0300_identity3 :: Cube -> Bool
245 -- prop_c0300_identity3 cube =
246 -- c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t1 1 2 0 0) / 2
248 -- t0 = tetrahedron0 (face0 cube)
249 -- t1 = tetrahedron0 (face2 (top cube))
250 -- t0' = Tetrahedron cube (v3 t0) (v2 t0) (v1 t0) (v0 t0)
251 -- t1' = Tetrahedron cube (v3 t1) (v2 t1) (v0 t1) (v1 t1)