List of polyhedra by facet layout (Meta, 12)
From Hi.gher. Space
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- | {|style='width:100%;' | + | <[#ontology [kind meta] [cats 3D Polytope Facet_Layout_Diagram]]> |
- | !style='width: | + | {|class='shapelist' style='width:100%;' |
- | !style='width: | + | !colspan='3'|Parent |
- | + | !colspan='3' class='key'|Elements | |
+ | !colspan='3'|Dual | ||
+ | |- | ||
+ | !style='width:10%;'|[[Facet layout]] | ||
+ | !style='width:20%;'|Name | ||
!style='width:8%;'|[[SSC2]] | !style='width:8%;'|[[SSC2]] | ||
- | !style='width:8%;'|Faces | + | !style='width:8%;' class='key'|Faces |
- | !style='width:8%;'|Edges | + | !style='width:8%;' class='key'|Edges |
- | !style='width:8%;'|Vertices | + | !style='width:8%;' class='key'|Vertices |
- | !style='width: | + | !style='width:10%;'|Facet layout |
- | !style='width: | + | !style='width:20%;'|Name |
+ | !style='width:8%;'|SSC2 | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row1' | ||
|{{FLD|a3|er|e3}} | |{{FLD|a3|er|e3}} | ||
- | |[[Tetrahedron]] | + | |[[Tetrahedron]]||Kt1 |
- | |- | + | |4||6||4 |
+ | |colspan='3'|''Self-dual'' | ||
+ | |- class='row2' | ||
+ | |{{FLD|a4|er|e3}} | ||
+ | |[[Cube]]||Ko1 | ||
+ | |6||12||8 | ||
|{{FLD|a3|er|e4}} | |{{FLD|a3|er|e4}} | ||
- | |[[Octahedron]] | + | |[[Octahedron]]||Ko4 |
- | | | + | |- class='row1' |
+ | |{{FLD|a5|er|e3}} | ||
+ | |[[Dodecahedron]]||Ki1 | ||
+ | |12||30||20 | ||
|{{FLD|a3|er|e5}} | |{{FLD|a3|er|e5}} | ||
- | |[[Icosahedron]] | + | |[[Icosahedron]]||Ki4 |
- | + | ||
- | + | ||
- | + | ||
- | + | ||
- | + | ||
- | + | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row2' | ||
|{{FLD|a3|i|a4|cr}} | |{{FLD|a3|i|a4|cr}} | ||
- | |[[ | + | |[[Stauromesohedron]]||Ko2 |
- | |- | + | |14||24||12 |
+ | |''Unknown'' | ||
+ | |[[Rhombic dodecahedron]]||''Unknown'' | ||
+ | |- class='row1' | ||
|{{FLD|a3|i|a5|cr}} | |{{FLD|a3|i|a5|cr}} | ||
- | |[[ | + | |[[Rhodomesohedron]]||Ki2 |
- | + | |32||60||30 | |
- | + | |''Unknown'' | |
- | + | |[[Rhombic triacontahedron]]||''Unknown'' | |
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row2' | ||
|{{FLD|a3|i|a3|er}} | |{{FLD|a3|i|a3|er}} | ||
- | |[[Tetrahedral truncate]] | + | |[[Tetrahedral truncate]]||Kt3 |
- | |- | + | |8||18||12 |
+ | |''Unknown'' | ||
+ | |[[Triakis tetrahedron]]||''Unknown'' | ||
+ | |- class='row1' | ||
|{{FLD|a3|i|a4|er}} | |{{FLD|a3|i|a4|er}} | ||
- | |[[Cubic truncate]] | + | |[[Cubic truncate]]||Ko3 |
- | |- | + | |14||36||24 |
+ | |''Unknown'' | ||
+ | |[[Triakis octahedron]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|a3|i|a5|er}} | |{{FLD|a3|i|a5|er}} | ||
- | |[[Dodecahedral truncate]] | + | |[[Dodecahedral truncate]]||Ki3 |
- | |- | + | |32||90||60 |
+ | |''Unknown'' | ||
+ | |[[Triakis icosahedron]]||''Unknown'' | ||
+ | |- class='row1' | ||
|{{FLD|a4|i|a3|er}} | |{{FLD|a4|i|a3|er}} | ||
- | |[[Octahedral truncate]] | + | |[[Octahedral truncate]]||Ko6 |
+ | |14||36||24 | ||
+ | |''Unknown'' | ||
+ | |[[Tetrakis hexahedron]]||''Unknown'' | ||
+ | |- class='row2' | ||
+ | |{{FLD|a5|i|a3|er}} | ||
+ | |[[Icosahedral truncate]]||Ki6 | ||
+ | |32||90||60 | ||
+ | |''Unknown'' | ||
+ | |[[Pentakis dodecahedron]]||''Unknown'' | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row1' | ||
+ | |{{FLD|a3|i|a2|er}} | ||
+ | |[[Triangular prism]]||+G3 | ||
+ | |5||9||6 | ||
+ | |''Unknown'' | ||
+ | |[[Triangular bipyramid]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|a5|i|a2|er}} | |{{FLD|a5|i|a2|er}} | ||
- | |[[Pentagonal prism]] | + | |[[Pentagonal prism]]||+G5 |
- | + | |7||15||10 | |
- | + | |''Unknown'' | |
- | + | |[[Pentagonal bipyramid]]||''Unknown'' | |
- | |- | + | |- class='row1' |
|{{FLD|a6|i|a2|er}} | |{{FLD|a6|i|a2|er}} | ||
- | |[[Hexagonal prism]] | + | |[[Hexagonal prism]]||+G6 |
- | |- | + | |8||18||12 |
+ | |''Unknown'' | ||
+ | |[[Hexagonal bipyramid]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|a8|i|a2|er}} | |{{FLD|a8|i|a2|er}} | ||
- | |[[Octagonal prism]] | + | |[[Octagonal prism]]||+G8 |
- | |- | + | |10||24||16 |
+ | |''Unknown'' | ||
+ | |[[Octagonal bipyramid]]||''Unknown'' | ||
+ | |- class='row1' | ||
|{{FLD|a10|i|a2|er}} | |{{FLD|a10|i|a2|er}} | ||
- | |[[Decagonal prism]] | + | |[[Decagonal prism]]||+G10 |
+ | |12||30||20 | ||
+ | |''Unknown'' | ||
+ | |[[Decagonal bipyramid]]||''Unknown'' | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row2' | ||
|{{FLD|a4|i|ade|cr|e4}} | |{{FLD|a4|i|ade|cr|e4}} | ||
- | |[[Square pyramid]] | + | |[[Square pyramid]]||&G4 |
+ | |5||8||5 | ||
+ | |colspan='3'|''Self-dual'' | ||
+ | |- class='row1' | ||
+ | |{{FLD|a5|i|ade|cr|e5}} | ||
+ | |[[Pentagonal pyramid]]||&G5 | ||
+ | |6||10||6 | ||
+ | |colspan='3'|''Self-dual'' | ||
+ | |- class='row2' | ||
+ | |{{FLD|a6|i|ade|cr|e6}} | ||
+ | |[[Hexagonal pyramid]]||&G6 | ||
+ | |7||12||7 | ||
+ | |colspan='3'|''Self-dual'' | ||
+ | |- class='row1' | ||
+ | |{{FLD|a8|i|ade|cr|e8}} | ||
+ | |[[Octagonal pyramid]]||&G8 | ||
+ | |9||16||9 | ||
+ | |colspan='3'|''Self-dual'' | ||
+ | |- class='row2' | ||
+ | |{{FLD|a10|i|ade|cr|e10}} | ||
+ | |[[Decagonal pyramid]]||&G10 | ||
+ | |11||20||11 | ||
+ | |colspan='3'|''Self-dual'' | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row1' | ||
|{{FLD|a4|i|ade|cr|e8}} | |{{FLD|a4|i|ade|cr|e8}} | ||
- | |[[Square antiprism]] | + | |[[Square antiprism]]||G4$H4 |
- | + | |10||16||8 | |
- | + | |''Unknown'' | |
- | + | |[[Tetragonal trapezohedron]]||''Unknown'' | |
- | |- | + | |- class='row2' |
|{{FLD|a5|i|ade|cr|e10}} | |{{FLD|a5|i|ade|cr|e10}} | ||
- | |[[Pentagonal antiprism]] | + | |[[Pentagonal antiprism]]||G5$H5 |
- | + | |12||20||10 | |
- | + | |''Unknown'' | |
- | + | |[[Pentagonal trapezohedron]]||''Unknown'' | |
- | |- | + | |- class='row1' |
|{{FLD|a6|i|ade|cr|e12}} | |{{FLD|a6|i|ade|cr|e12}} | ||
- | |[[Hexagonal antiprism]] | + | |[[Hexagonal antiprism]]||G6$H6 |
- | + | |16||28||14 | |
- | + | |''Unknown'' | |
- | + | |[[Hexagonal trapezohedron]]||''Unknown'' | |
- | |- | + | |- class='row2' |
|{{FLD|a8|i|ade|cr|e16}} | |{{FLD|a8|i|ade|cr|e16}} | ||
- | |[[Octagonal antiprism]] | + | |[[Octagonal antiprism]]||G8$H8 |
- | + | |20||36||18 | |
- | + | |''Unknown'' | |
- | + | |[[Octagonal trapezohedron]]||''Unknown'' | |
- | |- | + | |- class='row1' |
|{{FLD|a10|i|ade|cr|e20}} | |{{FLD|a10|i|ade|cr|e20}} | ||
- | |[[Decagonal antiprism]] | + | |[[Decagonal antiprism]]||G10$H10 |
+ | |24||44||22 | ||
+ | |''Unknown'' | ||
+ | |[[Decagonal trapezohedron]]||''Unknown'' | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row2' | ||
|{{FLD|left=e3|dsel|aq|dsrmel|adl|er}} | |{{FLD|left=e3|dsel|aq|dsrmel|adl|er}} | ||
- | |[[Trigonal expanded antitrapezohedron]]||Unknown | + | |[[Trigonal expanded antitrapezohedron]]||''Unknown'' |
- | |- | + | |12||24||14 |
+ | |{{FLD|a3|i|adr|edm|adl|er}} | ||
+ | |[[Triangular orthobicupola]]||''Unknown'' | ||
+ | |- class='row1' | ||
|{{FLD|left=e4|dsel|aq|dsrmel|adl|er}} | |{{FLD|left=e4|dsel|aq|dsrmel|adl|er}} | ||
- | |[[Tetragonal expanded antitrapezohedron]]||Unknown | + | |[[Tetragonal expanded antitrapezohedron]]||''Unknown'' |
- | |- | + | |16||32||18 |
+ | |{{FLD|a4|i|adr|edm|adl|er}} | ||
+ | |[[Square orthobicupola]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|left=e5|dsel|aq|dsrmel|adl|er}} | |{{FLD|left=e5|dsel|aq|dsrmel|adl|er}} | ||
- | |[[Pentagonal expanded antitrapezohedron]]||Unknown | + | |[[Pentagonal expanded antitrapezohedron]]||''Unknown'' |
+ | |20||40||22 | ||
+ | |{{FLD|a5|i|adr|edm|adl|er}} | ||
+ | |[[Pentagonal orthobicupola]]||''Unknown'' | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row1' | ||
|{{FLD|a3|i|ate|i|a4|cr}} | |{{FLD|a3|i|ate|i|a4|cr}} | ||
- | |[[ | + | |[[Snub staurohedron]]||Ko0 |
- | |- | + | |38||60||24 |
+ | |''Unknown'' | ||
+ | |[[Pentagonal icositetrahedron]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|a3|i|ate|i|a5|cr}} | |{{FLD|a3|i|ate|i|a5|cr}} | ||
- | |[[ | + | |[[Snub rhodohedron]]||Ki0 |
+ | |92||150||60 | ||
+ | |''Unknown'' | ||
+ | |[[Pentagonal hexecontahedron]]||''Unknown'' | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row1' | ||
|{{FLD|a3|i|a2|i|a4|cr}} | |{{FLD|a3|i|a2|i|a4|cr}} | ||
- | |[[ | + | |[[Stauroperihedron]]||Ko5 |
- | |- | + | |26||48||24 |
+ | |''Unknown'' | ||
+ | |[[Deltoidal icositetrahedron]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|a3|i|a2|i|a5|cr}} | |{{FLD|a3|i|a2|i|a5|cr}} | ||
- | |[[ | + | |[[Rhodoperihedron]]||Ki5 |
+ | |62||120||60 | ||
+ | |''Unknown'' | ||
+ | |[[Deltoidal hexecontahedron]]||''Unknown'' | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row1' | ||
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}} | |{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}} | ||
- | |[[ | + | |[[Stauropantohedron]]||Ko7 |
- | |- | + | |26||72||48 |
+ | |''Unknown'' | ||
+ | |[[Disdyakis dodecahedron]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}} | |{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}} | ||
- | |[[ | + | |[[Rhodopantohedron]]||Ki7 |
- | | | + | |62||180||120 |
- | + | |''Unknown'' | |
- | + | |[[Disdyakis triacontahedron]]||''Unknown'' | |
- | + | ||
- | + | ||
- | |[[ | + | |
- | + | ||
- | + | ||
- | + | ||
|- | |- | ||
+ | |class='cat' colspan='9'| | ||
+ | |- class='row1' | ||
|{{FLD|a3|i|adr|dm|adl|i|asr|dser}} | |{{FLD|a3|i|adr|dm|adl|i|asr|dser}} | ||
- | |[[Endotrikis antiprism]]||Unknown | + | |[[Endotrikis antiprism]]||''Unknown'' |
- | |- | + | |10||15||7 |
+ | |''Unknown'' | ||
+ | |[[Trigonal trapezosemipyramid]]||''Unknown'' | ||
+ | |- class='row2' | ||
|{{FLD|a4|i|adr|dm|adl|i|asr|dser}} | |{{FLD|a4|i|adr|dm|adl|i|asr|dser}} | ||
- | |[[Endotetrakis antiprism]]||Unknown||Unknown|| | + | |[[Endotetrakis antiprism]]||''Unknown'' |
+ | |13||20||9 | ||
+ | |''Unknown'' | ||
+ | |[[Tetragonal trapezosemipyramid]]||''Unknown'' | ||
+ | |- class='row1' | ||
+ | |{{FLD|a5|i|adr|dm|adl|i|asr|dser}} | ||
+ | |[[Endopentakis antiprism]]||''Unknown'' | ||
+ | |16||25||11 | ||
+ | |''Unknown'' | ||
+ | |[[Pentagonal trapezosemipyramid]]||''Unknown'' | ||
|- | |- | ||
- | |{{FLD| | + | |class='cat' colspan='9'| |
- | |[[ | + | |- class='row1' |
+ | |{{FLD|a3|i|adesr|di|asl|i|a3|cr}} | ||
+ | |[[Tridiminished icosahedron]]||''Unknown'' | ||
+ | |8||15||9 | ||
+ | |''Unknown'' | ||
+ | |''Unknown''||''Unknown'' | ||
+ | |- class='row2' | ||
+ | |{{FLD|a2tr|ti|asrtm|ditm|aqtm|editm|atlsl|cr}} | ||
+ | |[[Bilunabirotunda]]||''Unknown'' | ||
+ | |14||26||14 | ||
+ | |''Unknown'' | ||
+ | |''Unknown''||''Unknown'' | ||
|} | |} | ||
[[Category:Trishapes|$]] | [[Category:Trishapes|$]] |