List of polyhedra by facet layout (Meta, 12)
From Hi.gher. Space
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- | {|style='width:100%;' | + | {|class='shapelist' style='width:100%;' |
- | !style='width: | + | !colspan='3'|Parent |
- | !style='width: | + | !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 |
- | + | ||
- | + | ||
- | + | ||
- | + | ||
- | + | ||
- | + | ||
|- | |- | ||
|{{FLD|a3|i|a4|cr}} | |{{FLD|a3|i|a4|cr}} | ||
- | |[[Cuboctahedron]] | + | |[[Cuboctahedron]]||Ko2||14||24||12||[[Rhombic dodecahedron]] |
|- | |- | ||
|{{FLD|a3|i|a5|cr}} | |{{FLD|a3|i|a5|cr}} | ||
- | |[[Icosidodecahedron]] | + | |[[Icosidodecahedron]]||Ki2||32||60||30||[[Rhombic triacontahedron]] |
|- | |- | ||
|{{FLD|a3|i|a2|er}} | |{{FLD|a3|i|a2|er}} | ||
- | |[[Triangular prism]] | + | |[[Triangular prism]]||+G3||5||9||6||[[Triangular bipyramid]] |
|- | |- | ||
|{{FLD|a3|i|a3|er}} | |{{FLD|a3|i|a3|er}} | ||
- | |[[Tetrahedral truncate]] | + | |[[Tetrahedral truncate]]||Kt3||8||18||12||[[Triakis tetrahedron]] |
|- | |- | ||
|{{FLD|a3|i|a4|er}} | |{{FLD|a3|i|a4|er}} | ||
- | |[[Cubic truncate]] | + | |[[Cubic truncate]]||Ko3||14||36||24||[[Triakis octahedron]] |
|- | |- | ||
|{{FLD|a3|i|a5|er}} | |{{FLD|a3|i|a5|er}} | ||
- | |[[Dodecahedral truncate]] | + | |[[Dodecahedral truncate]]||Ki3||32||90||60||[[Triakis icosahedron]] |
|- | |- | ||
|{{FLD|a4|i|a3|er}} | |{{FLD|a4|i|a3|er}} | ||
- | |[[Octahedral truncate]] | + | |[[Octahedral truncate]]||Ko6||14||36||24||[[Tetrakis hexahedron]] |
|- | |- | ||
|{{FLD|a5|i|a2|er}} | |{{FLD|a5|i|a2|er}} | ||
- | |[[Pentagonal prism]] | + | |[[Pentagonal prism]]||+G5||7||15||10||[[Pentagonal bipyramid]] |
|- | |- | ||
|{{FLD|a5|i|a3|er}} | |{{FLD|a5|i|a3|er}} | ||
- | |[[Icosahedral truncate]] | + | |[[Icosahedral truncate]]||Ki6||32||90||60||[[Pentakis dodecahedron]] |
|- | |- | ||
|{{FLD|a6|i|a2|er}} | |{{FLD|a6|i|a2|er}} | ||
- | |[[Hexagonal prism]] | + | |[[Hexagonal prism]]||+G6||8||18||12||[[Hexagonal bipyramid]] |
|- | |- | ||
|{{FLD|a8|i|a2|er}} | |{{FLD|a8|i|a2|er}} | ||
- | |[[Octagonal prism]] | + | |[[Octagonal prism]]||+G8||10||24||16||[[Octagonal bipyramid]] |
|- | |- | ||
|{{FLD|a10|i|a2|er}} | |{{FLD|a10|i|a2|er}} | ||
- | |[[Decagonal prism]] | + | |[[Decagonal prism]]||+G10||12||30||20||[[Decagonal bipyramid]] |
|- | |- | ||
|{{FLD|a4|i|ade|cr|e4}} | |{{FLD|a4|i|ade|cr|e4}} | ||
- | |[[Square pyramid]] | + | |[[Square pyramid]]||&G4||5||8||5||Self-dual |
|- | |- | ||
|{{FLD|a4|i|ade|cr|e8}} | |{{FLD|a4|i|ade|cr|e8}} | ||
- | |[[Square antiprism]] | + | |[[Square antiprism]]||G4$H4||10||16||8||[[Tetragonal trapezohedron]] |
|- | |- | ||
|{{FLD|a5|i|ade|cr|e5}} | |{{FLD|a5|i|ade|cr|e5}} | ||
- | |[[Pentagonal pyramid]] | + | |[[Pentagonal pyramid]]||&G5||6||10||6||Self-dual |
|- | |- | ||
|{{FLD|a5|i|ade|cr|e10}} | |{{FLD|a5|i|ade|cr|e10}} | ||
- | |[[Pentagonal antiprism]] | + | |[[Pentagonal antiprism]]||G5$H5||12||20||10||[[Pentagonal trapezohedron]] |
|- | |- | ||
|{{FLD|a6|i|ade|cr|e6}} | |{{FLD|a6|i|ade|cr|e6}} | ||
- | |[[Hexagonal pyramid]] | + | |[[Hexagonal pyramid]]||&G6||7||12||7||Self-dual |
|- | |- | ||
|{{FLD|a6|i|ade|cr|e12}} | |{{FLD|a6|i|ade|cr|e12}} | ||
- | |[[Hexagonal antiprism]] | + | |[[Hexagonal antiprism]]||G6$H6||16||28||14||[[Hexagonal trapezohedron]] |
|- | |- | ||
|{{FLD|a8|i|ade|cr|e8}} | |{{FLD|a8|i|ade|cr|e8}} | ||
- | |[[Octagonal pyramid]] | + | |[[Octagonal pyramid]]||&G8||9||16||9||Self-dual |
|- | |- | ||
|{{FLD|a8|i|ade|cr|e16}} | |{{FLD|a8|i|ade|cr|e16}} | ||
- | |[[Octagonal antiprism]] | + | |[[Octagonal antiprism]]||G8$H8||20||36||18||[[Octagonal trapezohedron]] |
|- | |- | ||
|{{FLD|a10|i|ade|cr|e10}} | |{{FLD|a10|i|ade|cr|e10}} | ||
- | |[[Decagonal pyramid]] | + | |[[Decagonal pyramid]]||&G10||11||20||11||Self-dual |
|- | |- | ||
|{{FLD|a10|i|ade|cr|e20}} | |{{FLD|a10|i|ade|cr|e20}} | ||
- | |[[Decagonal antiprism]] | + | |[[Decagonal antiprism]]||G10$H10||24||44||22||[[Decagonal trapezohedron]] |
|- | |- | ||
|{{FLD|left=e3|dsel|aq|dsrmel|adl|er}} | |{{FLD|left=e3|dsel|aq|dsrmel|adl|er}} | ||
- | |[[Trigonal expanded antitrapezohedron]] | + | |[[Trigonal expanded antitrapezohedron]]||Unknown||12||24||14||[[Triangular orthobicupola]] |
|- | |- | ||
|{{FLD|left=e4|dsel|aq|dsrmel|adl|er}} | |{{FLD|left=e4|dsel|aq|dsrmel|adl|er}} | ||
- | |[[Tetragonal expanded antitrapezohedron]] | + | |[[Tetragonal expanded antitrapezohedron]]||Unknown||16||32||18||[[Square orthobicupola]] |
|- | |- | ||
|{{FLD|left=e5|dsel|aq|dsrmel|adl|er}} | |{{FLD|left=e5|dsel|aq|dsrmel|adl|er}} | ||
- | |[[Pentagonal expanded antitrapezohedron]] | + | |[[Pentagonal expanded antitrapezohedron]]||Unknown||20||40||22||[[Pentagonal orthobicupola]] |
|- | |- | ||
|{{FLD|a3|i|ate|i|a4|cr}} | |{{FLD|a3|i|ate|i|a4|cr}} | ||
- | |[[Cubic snub]] | + | |[[Cubic snub]]||Ko0||38||60||24||[[Pentagonal icositetrahedron]] |
|- | |- | ||
|{{FLD|a3|i|ate|i|a5|cr}} | |{{FLD|a3|i|ate|i|a5|cr}} | ||
- | |[[Dodecahedral snub]] | + | |[[Dodecahedral snub]]||Ki0||92||150||60||[[Pentagonal hexecontahedron]] |
|- | |- | ||
|{{FLD|a3|i|a2|i|a4|cr}} | |{{FLD|a3|i|a2|i|a4|cr}} | ||
- | |[[Cuboctahedral rectate]] | + | |[[Cuboctahedral rectate]]||Ko5||26||48||24||[[Deltoidal icositetrahedron]] |
|- | |- | ||
|{{FLD|a3|i|a2|i|a5|cr}} | |{{FLD|a3|i|a2|i|a5|cr}} | ||
- | |[[Icosidodecahedral rectate]] | + | |[[Icosidodecahedral rectate]]||Ki5||62||120||60||[[Deltoidal hexecontahedron]] |
|- | |- | ||
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}} | |{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}} | ||
- | |[[Cuboctahedral truncate]] | + | |[[Cuboctahedral truncate]]||Ko7||26||72||48||[[Disdyakis dodecahedron]] |
|- | |- | ||
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}} | |{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}} | ||
- | |[[Icosidodecahedral truncate]] | + | |[[Icosidodecahedral truncate]]||Ki7||62||180||120||[[Disdyakis triacontahedron]] |
|- | |- | ||
|{{FLD|a3|i|adr|edm|adl|er}} | |{{FLD|a3|i|adr|edm|adl|er}} | ||
- | |[[Triangular orthobicupola]] | + | |[[Triangular orthobicupola]]||Unknown||14||24||12||[[Trigonal expanded antitrapezohedron]] |
|- | |- | ||
|{{FLD|a4|i|adr|edm|adl|er}} | |{{FLD|a4|i|adr|edm|adl|er}} | ||
- | |[[Square orthobicupola]] | + | |[[Square orthobicupola]]||Unknown||18||32||16||[[Tetragonal expanded antitrapezohedron]] |
|- | |- | ||
|{{FLD|a5|i|adr|edm|adl|er}} | |{{FLD|a5|i|adr|edm|adl|er}} | ||
- | |[[Pentagonal orthobicupola]] | + | |[[Pentagonal orthobicupola]]||Unknown||22||40||20||[[Pentagonal expanded antitrapezohedron]] |
|- | |- | ||
|{{FLD|a3|i|adr|dm|adl|i|asr|dser}} | |{{FLD|a3|i|adr|dm|adl|i|asr|dser}} | ||
- | |[[Endotrikis antiprism]] | + | |[[Endotrikis antiprism]]||Unknown||10||15||7||[[Trigonal trapezosemipyramid]] |
|- | |- | ||
|{{FLD|a4|i|adr|dm|adl|i|asr|dser}} | |{{FLD|a4|i|adr|dm|adl|i|asr|dser}} | ||
- | |[[Endotetrakis antiprism]] | + | |[[Endotetrakis antiprism]]||Unknown||13||20||9||[[Tetragonal trapezosemipyramid]] |
|- | |- | ||
|{{FLD|a5|i|adr|dm|adl|i|asr|dser}} | |{{FLD|a5|i|adr|dm|adl|i|asr|dser}} | ||
- | |[[Endopentakis antiprism]] | + | |[[Endopentakis antiprism]]||Unknown||16||25||11||[[Pentagonal trapezosemipyramid]] |
|} | |} | ||
[[Category:Trishapes|$]] | [[Category:Trishapes|$]] |