Segmentochoron construction table (no ontology)

From Hi.gher. Space

(Difference between revisions)

Revision as of 10:51, 15 March 2016

This table gives every combination of 3D figures to form segmentochora as found by Klitzing.

For those segmentochoron that can be constructed in more than one way, all ways are listed. Also, for those that are not prisms, both the construction giving by Klitzing and the construction with the two bases flipped is listed. The symmetry groups of the bases are also given. This helps in finding patterns by sorting the table.

The notation used in the "Base" column is either SSC2 notation or Jn for a Johnson solid.

Base 1Base 2Sym 1Sym 2Result (K4.n)
M0Kt1C1Td1
Kt1M0TdC11
M1G3@pD1D31
G3@pM1D3D11
Kt1Kt1@dTdTd2
Kt1@dKt1TdTd2
M0Ko4C1Oh3
Ko4M0OhC13
G3Kt1@gD3Td3
Kt1@gG3TdD33
M0&G4C1C4v4
&G4M0C4vC14
M1Kt1D1Td4
Kt1M1TdD14
G3G3@iD3D34
G3@iG3D3D34
M1G4@pD1D44
G4@pM1D4D14
Kt1Ko4TdOh5
Ko4Kt1OhTd5
Kt1&G4TdC4v6
&G4Kt1C4vTd6
G3Ko4D3Oh6
Ko4G3OhD36
G3+G3@gD3D3h6
G3@gG3D3hD36
M1&G4D1C4v7
&G4M1C4vD17
G3Kt1D3Td7
Kt1G3TdD37
M0+G3C1D3h7
G3M0D3hC17
G3G4@oD3D47
G4@oG3D4D37
G3&G4D3C4v8
&G4G3C4vD38
G4Kt1D4Td8
Kt1G4TdD48
M1+G3@oD1D3h8
G3@oM1D3hD18
Kt1Kt1TdTd9
M1+G3@lD1D3h9
G3@lM1D3hD19
G4G4@oD4D49
G4@oG4D4D49
G3+G3D3D3h10
G3G3D3hD310
Ko4Ko4OhOh11
G3+G3@gD3hD3h11 G3@g+G3D3hD3h11
&G4&G4C4vC4v12
G4+G3D4D3h12
G3G4D3hD412
M1Ko1D1Oh12
Ko1M1OhD112
G3+G3@roD3hD3h13 G3@ro+G3D3hD3h13
G4G4$H4D4D4d14
G4$H4G4D4dD414
G4Ko1@gD4Oh14
Ko1@gG4OhD414
Ko4Ko1OhOh15
Ko1Ko4OhOh15
&G4Ko1@gC4vOh16
Ko1@g&G4OhC4v16
G4&G4@gD4C4v17
&G4@gG4C4vD417
M0G4$H4C1D4d17
G4$H4M0D4dC117
G3+G3D3hD3h18
G4Ko1D4Oh18
Ko1G4OhD418
G4$H4G4$H4D4dD4d19
Ko1Ko1@gOhOh19
Ko1@gKo1OhOh19
Ko1Ko1OhOh20
Ko1Ki4OhIh21
Ki4Ko1IhOh21
G5G5$H5D5D5d22
G5$H5G5D5dD522
G5+G5@gD5D5h22
G5@gG5D5hD522
Kt1Ko2TdOh23
Ko2Kt1OhTd23
Kt1J3TdC3v24
J3Kt1C3vTd24
G3J3D3C3v25
J3G3C3vD325
G6+G3D6D3h25
G3G6D3hD625
G4&G4D4C4v26
&G4G4C4vD426
M0Ko1C1Oh26
Ko1M0OhC126
G3J3@gD3C3v27
J3@gG3C3vD327
G6Ko4D6Oh27
Ko4G6OhD627
G4Ko2D4Oh28
Ko2G4OhD428
Ko4Ko2OhOh29
Ko2Ko4OhOh29
Ko4J3OhC3v30
J3Ko4C3vOh30
&G4Ko2C4vOh31
Ko2&G4OhC4v31
&G4J3C4vC3v32
J3&G4C3vC4v32
G3J63D3C3v33
J63G3C3vD333
G5+G5D5D5h34
G5G5D5hD534
Ko1Ko2OhOh35
Ko2Ko1OhOh35
Ki4Ki4IhIh36
J11J11C5vC5v37
&G5&G5C5vC5v38
M1+G5D1D5h38
G5M1D5hD138
G5$H5G5$H5D5dD5d39
G5+G5@gD5hD5h39 G5@g+G5D5hD5h39
J62J62C2vC2v40
J63J63C3vC3v41
&G5&G5C5vC5v42
Ko2Ko2OhOh43
J27J27D3hD3h44
J3J3C3vC3v45
G3G6D3hD645
G6+G3D6D3h45
G6G6$H6D6D6d46
G6$H6G6D6dD646
G6+G6@gD6D6h46
G6@gG6D6hD646
G6+G6D6D6h47
G6G6D6hD647
Ko2Kt3OhTd48
Kt3Ko2TdOh48
J27Kt3D3hTd49
Kt3J27TdD3h49
J3Kt3C3vTd50
Kt3J3TdC3v50
G6J3D6C3v51
J3G6C3vD651
G3+G6D3D6h51
G6G3D6hD351
Ko4Kt3OhTd52
Kt3Ko4TdOh52
G6$H6G6$H6D6dD6d53
G6+G6@gD6hD6h53 G6@g+G6D6hD6h53 G6+G6D6hD6h54
Kt3Kt3@vTdTd55
Kt3@vKt3TdTd55
Kt1Kt3TdTd56
Kt3Kt1TdTd56
Kt3Kt3TdTd57
G8G8$H8D8D8d58
G8$H8G8D8dD858
G8+G8@gD8D8h58
G8@gG8D8hD858
G8+G8D8D8h59
G8G8D8hD859
Ko0Ko0OO60
Ko2Ko5OhOh61
Ko5Ko2OhOh61
Ko2J19OhC4v62
J19Ko2C4vOh62
Ko2+G8OhD8h63
G8Ko2D8hOh63
G4J4@gD4C4v64
J4@gG4C4vD464
G8G4$H4D8D4d64
G4$H4G8D4dD864
G8$H8G8$H8D8dD8d65
G8+G8@gD8hD8h65 G8@g+G8D8hD8h65
Ko5Ko5OhOh66
J37J37D4dD4d67
J19J19C4vC4v68
J4J4C4vC4v69
Ko1+G8OhD8h69
G8Ko1D8hOh69 G8+G8D8hD8h70
Ko1Ko5OhOh71
Ko5Ko1OhOh71
Ko1J19OhC4v72
J19Ko1C4vOh72
G4J4D4C4v73
J4G4C4vD473
G8Ko1D8Oh73
Ko1G8OhD873
Ki1Ki1IhIh74
Ko5Ko6OhOh75
Ko6Ko5OhOh75
Kt3Ko6TdOh76
Ko6Kt3OhTd76
Ki1Ki2IhIh77
Ki2Ki1IhIh77
Ki4Ki1IhIh78
Ki1Ki4IhIh78
J11Ki1C5vIh79
Ki1J11IhC5v79
G5&G5@gD5C5v80
&G5@gG5C5vD580
M0G5$H5C1D5d80
G5$H5M0D5dC180
G5$H5Ki1D5dIh81
Ki1G5$H5IhD5d81
J62Ki1C2vIh82
Ki1J62IhC2v82
J63Ki1C3vIh83
Ki1J63IhC3v83
M0Ki4C1Ih84
Ki4M0IhC184
M0J11C1C5v85
J11M0C5vC185
M0&G5C1C5v86
&G5M0C5vC186
M1G5@pD1D586
G5@pM1D5D186
M0J62C1C2v87
J62M0C2vC187
M0J63C1C3v88
J63M0C3vC188
Ko6Ko6OhOh89
Ko2Ko2OhOh90
J34J34D5hD5h91
J6J6C5vC5v92
G10G10$H10D10D10d93
G10$H10G10D10dD1093
G10+G10@gD10D10h93
G10@gG10D10hD1093
G10+G10D10D10h94
G10G10D10hD1094
Ko2Ko6OhOh95
Ko6Ko2OhOh95
G10$H10G10$H10D10dD10d96
G10+G10@gD10hD10h96 G10@g+G10D10hD10h96 G10+G10D10hD10h97
Ko6Ko3OhOh98
Ko3Ko6OhOh98
Ko3Ko3OhOh99
Ko5Ko3OhOh100
Ko3Ko5OhOh100
J37Ko3D4dOh101
Ko3J37OhD4d101
Ko5Ko3@gOhOh102
Ko3@gKo5OhOh102
J19Ko3C4vOh103
Ko3J19OhC4v103
J19Ko3@gC4vOh104
Ko3@gJ19OhC4v104
G8J4D8C4v105
J4G8C4vD8105
G4+G8D4D8h105
G8G4D8hD4105 G8Ko3D8hOh106
Ko3+G8OhD8h106
Ko4Ko5OhOh107
Ko5Ko4OhOh107
&G4J19C4vC4v108
J19&G4C4vC4v108
&G4J4C4vC4v109
J4&G4C4vC4v109
Ki0Ki0II110
Ki5Ki5IhIh111
J72J72C5vC5v112
J73J73D5dD5d113
J74J74C2vC2v114
J75J75C3vC3v115
J76J76C5vC5v116
J5J5C5vC5v117
G5+G10D5hD10h117 G10+G5D10hD5h117
J77J77C5vC5v118
J78J78CsCs119
J79J79CsCs120
J80J80D5dD5d121
J81J81C2vC2v122
J82J82CsCs123
J83J83C3vC3v124
Ko7Ko7OhOh125
Ki5Ki6IhIh126
Ki6Ki5IhIh126
Ki6Ki6IhIh127
Ko3Ko7OhOh128
Ko7Ko3OhOh128
Ko2Ko3OhOh129
Ko3Ko2OhOh129
Ki3Ki3IhIh130
Ki2Ki5IhIh131
Ki5Ki2IhIh131
Ki2J76IhC5v132
J76Ki2C5vIh132
G5J5@gD5C5v133
J5@gG5C5vD5133
G10G5$H5D10D5d133
G5$H5G10D5dD10133
Ki2J80IhD5d134
J80Ki2D5dIh134
Ki2J81IhC2v135
J81Ki2C2vIh135
Ki2J83IhC3v136
J83Ki2C3vIh136
Ki4Ki2IhIh137
Ki2Ki4IhIh137
J11Ki2C5vIh138
Ki2J11IhC5v138
&G5J6C5vC5v139
J6&G5C5vC5v139
J11J6C5vC5v140
J6J11C5vC5v140
G5&G5D5C5v141
&G5G5C5vD5141
M0+G5C1D5h141
G5M0D5hC1141
G5$H5Ki2D5dIh142
Ki2G5$H5IhD5d142
J62Ki2C2vIh143
Ki2J62IhC2v143
G5$H5J6D5dC5v144
J6G5$H5C5vD5d144
J62J6C2vC5v145
J6J62C5vC2v145
G5J6D5C5v146
J6G5C5vD5146
J63Ki2C3vIh147
Ki2J63IhC3v147
J63J6C3vC5v148
J6J63C5vC3v148
Ko6Ko7OhOh149
Ko7Ko6OhOh149
Ki7Ki7IhIh150
Ki6Ki3IhIh151
Ki3Ki6IhIh151
Ki4Ki5IhIh152
Ki5Ki4IhIh152
Ki1J76IhC5v153
J76Ki1C5vIh153
G5J5D5C5v154
J5G5C5vD5154
G10+G5D10D5h154
G5G10D5hD10154
Ki1J80IhD5d155
J80Ki1D5dIh155
Ki1J81IhC2v156
J81Ki1C2vIh156
Ki1J83IhC3v157
J83Ki1C3vIh157
Ki2Ki6IhIh158
Ki6Ki2IhIh158
Ki5Ki3IhIh159
Ki3Ki5IhIh159
J72Ki3C5vIh160
Ki3J72IhC5v160
J73Ki3D5dIh161
Ki3J73IhD5d161
J74Ki3C2vIh162
Ki3J74IhC2v162
J75Ki3C3vIh163
Ki3J75IhC3v163
J76Ki3C5vIh164
Ki3J76IhC5v164
G10J5D10C5v165
J5G10C5vD10165
G5+G10D5D10h165
G10G5D10hD5165
J77Ki3C5vIh166
Ki3J77IhC5v166
J78Ki3CsIh167
Ki3J78IhCs167
J79Ki3CsIh168
Ki3J79IhCs168
J80Ki3D5dIh169
Ki3J80IhD5d169
J81Ki3C2vIh170
Ki3J81IhC2v170
J82Ki3CsIh171
Ki3J82IhCs171
J83Ki3C3vIh172
Ki3J83IhC3v172
Ki3Ki7IhIh173
Ki7Ki3IhIh173