Steriruncinated 6-simplex |
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Rank | 6 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Copal |
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Coxeter diagram | x3o3o3x3x3o () |
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Elements |
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Peta | 35 triangular-tetrahedral duoprisms, 35 triangular-truncated tetrahedral duoprisms, 21 decachoric prisms, 7 bitruncated hexatera, 7 celliprismated hexatera |
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Tera | 105 tetrahedral prisms, 140 triangular duoprisms, 140 triangular-hexagonal duoprisms, 42 truncated pentachora, 21 small prismatodecachora, 105+105 truncated tetrahedral prisms, 42 decachora |
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Cells | 105+105 tetrahedra, 210+210+210+420 triangular prisms, 420 hexagonal prisms, 105+210 truncated tetrahedra |
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Faces | 140+420+420 triangles, 630+630 squares, 420 hexagons |
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Edges | 420+630+630 |
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Vertices | 420 |
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Vertex figure | Skewed Triangular antiprismatic scalene, base edge lengths 1 and √2, opposite edge length 1, lacing lengths √2 and √3 |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Dipetal angles | Tratet–triddip–tratut: |
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| Decap–tuttip–tratut: |
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| Bittix–deca–decap: |
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| Cappix–tepe–tratet: |
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| Cappix–thiddip–tratut: |
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| Cappix–tuttip–decap: |
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| Cappix–tip–bittix: |
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| Cappix–spid–cappix: |
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Central density | 1 |
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Number of external pieces | 105 |
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Level of complexity | 120 |
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Related polytopes |
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Army | Copal |
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Regiment | Copal |
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Conjugate | None |
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Abstract & topological properties |
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Flag count | 604800 |
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Euler characteristic | 0 |
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Orientable | Yes |
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Properties |
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Symmetry | A6, order 5040 |
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Convex | Yes |
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Nature | Tame |
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The steriruncinated 6-simplex, also called the steriruncinated heptapeton, celliprismated heptapeton, or copal, is a convex uniform 6-polytope. It consists of 7 steritruncated 5-simplices, 7 bitruncated 5-simplices, 21 decachoric prisms, 35 triangular-tetrahedral duoprisms, and 35 triangular-truncated tetrahedral duoprisms. 2 steritruncated 5-simplices, 1 bitruncated 5-simplex, 3 decachoric prisms, 1 triangular-tetrahedral duoprism, and 3 triangular-truncated tetrahedral duoprisms join at each vertex. As the name suggests, it is the steriruncination of the 6-simplex.
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A5 orthographic projection
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The vertices of a steriruncinated 6-simplex of edge length 1 can be given in 7 dimensions as all permutations of:
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The regiment of the celliprismated heptapeton contains 7 uniform members.
truncations |
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Name | OBSA | Schläfli symbol | CD diagram | Image |
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6-simplex | hop | {3,3,3,3,3} | | |
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Rectified 6-simplex | ril | r{3,3,3,3,3} | | |
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Birectified 6-simplex | bril | t2{3,3,3,3,3} | | |
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Truncated 6-simplex | til | t{3,3,3,3,3} | | |
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Cantellated 6-simplex | sril | rr{3,3,3,3,3} | | |
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Runcinated 6-simplex | spil | t0,3{3,3,3,3,3} | | |
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Stericated 6-simplex | scal | t0,4{3,3,3,3,3} | | |
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Pentellated 6-simplex | staf | t0,5{3,3,3,3,3} | | |
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Bitruncated 6-simplex | batal | t1,2{3,3,3,3,3} | | |
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Bicantellated 6-simplex | sabril | t1,3{3,3,3,3,3} | | |
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Biruncinated 6-simplex | sibpof | t1,4{3,3,3,3,3} | | |
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Tritruncated 6-simplex | fe | t2,3{3,3,3,3,3} | | |
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Cantitruncated 6-simplex | gril | tr{3,3,3,3,3} | | |
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Runcitruncated 6-simplex | patal | t0,1,3{3,3,3,3,3} | | |
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Steritruncated 6-simplex | catal | t0,1,4{3,3,3,3,3} | | |
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Pentitruncated 6-simplex | tocal | t0,1,5{3,3,3,3,3} | | |
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Runcicantellated 6-simplex | pril | t0,2,3{3,3,3,3,3} | | |
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Stericantellated 6-simplex | cral | t0,2,4{3,3,3,3,3} | | |
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Penticantellated 6-simplex | topal | t0,2,5{3,3,3,3,3} | | |
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Steriruncinated 6-simplex | copal | t0,3,4{3,3,3,3,3} | | |
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Bicantitruncated 6-simplex | gabril | t1,2,3{3,3,3,3,3} | | |
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Biruncitruncated 6-simplex | bapril | t1,2,4{3,3,3,3,3} | | |
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Runcicantitruncated 6-simplex | gapil | t0,1,2,3{3,3,3,3,3} | | |
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Stericantitruncated 6-simplex | cagral | t0,1,2,4{3,3,3,3,3} | | |
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Penticantitruncated 6-simplex | togral | t0,1,2,5{3,3,3,3,3} | | |
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Steriruncitruncated 6-simplex | captal | t0,1,3,4{3,3,3,3,3} | | |
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Pentiruncitruncated 6-simplex | tocral | t0,1,3,5{3,3,3,3,3} | | |
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Pentisteritruncated 6-simplex | tactaf | t0,1,4,5{3,3,3,3,3} | | |
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Steriruncicantellated 6-simplex | copril | t0,2,3,4{3,3,3,3,3} | | |
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Pentiruncicantellated 6-simplex | taporf | t0,2,3,5{3,3,3,3,3} | | |
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Biruncicantitruncated 6-simplex | gibpof | t1,2,3,4{3,3,3,3,3} | | |
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Steriruncicantitruncated 6-simplex | gacal | t0,1,2,3,4{3,3,3,3,3} | | |
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Pentiruncicantitruncated 6-simplex | tagopal | t0,1,2,3,5{3,3,3,3,3} | | |
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Pentistericantitruncated 6-simplex | tacogral | t0,1,2,4,5{3,3,3,3,3} | | |
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Omnitruncated 6-simplex | gotaf | t0,1,2,3,4,5{3,3,3,3,3} | | |
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