List of polyhedra by facet layout (Meta, 12)
From Hi.gher. Space
(Difference between revisions)
m (fix FLD) |
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!style='width:16%;'|Dual | !style='width:16%;'|Dual | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|e|e3}} |
|[[Tetrahedron]]||4,0||Kt1||4||6||4||None||Self-dual | |[[Tetrahedron]]||4,0||Kt1||4||6||4||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|e|e4}} |
|[[Octahedron]]||6,0||Ko4||8||12||6||None||[[Cube]] | |[[Octahedron]]||6,0||Ko4||8||12||6||None||[[Cube]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|e|e5}} |
|[[Icosahedron]]||10,2||Ki4||20||30||12||None||[[Dodecahedron]] | |[[Icosahedron]]||10,2||Ki4||20||30||12||None||[[Dodecahedron]] | ||
|- | |- | ||
- | |{{FLD|a4| | + | |{{FLD|a4|e|e3}} |
|[[Cube]]||6,2||Ko1||6||12||8||[[Tetrahedron]]||[[Octahedron]] | |[[Cube]]||6,2||Ko1||6||12||8||[[Tetrahedron]]||[[Octahedron]] | ||
|- | |- | ||
- | |{{FLD|a5| | + | |{{FLD|a5|e|e3}} |
|[[Dodecahedron]]||10,10,0||Ki1||12||30||20||None||[[Icosahedron]] | |[[Dodecahedron]]||10,10,0||Ki1||12||30||20||None||[[Icosahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a4|cr}} |
|[[Cuboctahedron]]||Unknown||Ko2||14||24||12||None||[[Rhombic dodecahedron]] | |[[Cuboctahedron]]||Unknown||Ko2||14||24||12||None||[[Rhombic dodecahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a5|cr}} |
|[[Icosidodecahedron]]||Unknown||Ki2||32||60||30||None||[[Rhombic triacontahedron]] | |[[Icosidodecahedron]]||Unknown||Ki2||32||60||30||None||[[Rhombic triacontahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a2|e}} |
|[[Triangular prism]]||Unknown||+G3||5||9||6||None||[[Triangular bipyramid]] | |[[Triangular prism]]||Unknown||+G3||5||9||6||None||[[Triangular bipyramid]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a3|e}} |
|[[Tetrahedral truncate]]||Unknown||Kt3||8||18||12||None||[[Triakis tetrahedron]] | |[[Tetrahedral truncate]]||Unknown||Kt3||8||18||12||None||[[Triakis tetrahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a4|e}} |
|[[Cubic truncate]]||Unknown||Ko3||14||36||24||None||[[Triakis octahedron]] | |[[Cubic truncate]]||Unknown||Ko3||14||36||24||None||[[Triakis octahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a5|e}} |
|[[Dodecahedral truncate]]||Unknown||Ki3||32||90||60||None||[[Triakis icosahedron]] | |[[Dodecahedral truncate]]||Unknown||Ki3||32||90||60||None||[[Triakis icosahedron]] | ||
|- | |- | ||
- | |{{FLD|a4| | + | |{{FLD|a4|i|a3|e}} |
|[[Octahedral truncate]]||Unknown||Ko6||14||36||24||[[Icosahedron]]||[[Tetrakis hexahedron]] | |[[Octahedral truncate]]||Unknown||Ko6||14||36||24||[[Icosahedron]]||[[Tetrakis hexahedron]] | ||
|- | |- | ||
- | |{{FLD|a5| | + | |{{FLD|a5|i|a2|e}} |
|[[Pentagonal prism]]||Unknown||+G5||7||15||10||None||[[Pentagonal bipyramid]] | |[[Pentagonal prism]]||Unknown||+G5||7||15||10||None||[[Pentagonal bipyramid]] | ||
|- | |- | ||
- | |{{FLD|a5| | + | |{{FLD|a5|i|a3|e}} |
|[[Icosahedral truncate]]||Unknown||Ki6||32||90||60||None||[[Pentakis dodecahedron]] | |[[Icosahedral truncate]]||Unknown||Ki6||32||90||60||None||[[Pentakis dodecahedron]] | ||
|- | |- | ||
- | |{{FLD|a6| | + | |{{FLD|a6|i|a2|e}} |
|[[Hexagonal prism]]||Unknown||+G6||8||18||12||[[Octahedron]]||[[Hexagonal bipyramid]] | |[[Hexagonal prism]]||Unknown||+G6||8||18||12||[[Octahedron]]||[[Hexagonal bipyramid]] | ||
|- | |- | ||
- | |{{FLD|a8| | + | |{{FLD|a8|i|a2|e}} |
|[[Octagonal prism]]||Unknown||+G8||10||24||16||[[Square antiprism]]||[[Octagonal bipyramid]] | |[[Octagonal prism]]||Unknown||+G8||10||24||16||[[Square antiprism]]||[[Octagonal bipyramid]] | ||
|- | |- | ||
- | |{{FLD|a10| | + | |{{FLD|a10|i|a2|e}} |
|[[Decagonal prism]]||Unknown||+G10||12||30||20||[[Pentagonal antiprism]]||[[Decagonal bipyramid]] | |[[Decagonal prism]]||Unknown||+G10||12||30||20||[[Pentagonal antiprism]]||[[Decagonal bipyramid]] | ||
|- | |- | ||
- | |{{FLD|a4| | + | |{{FLD|a4|i|ade|cr|e4}} |
|[[Square pyramid]]||Unknown||&G4||5||8||5||None||Self-dual | |[[Square pyramid]]||Unknown||&G4||5||8||5||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a4| | + | |{{FLD|a4|i|ade|cr|e8}} |
|[[Square antiprism]]||Unknown||G4$H4||10||16||8||None||[[Tetragonal trapezohedron]] | |[[Square antiprism]]||Unknown||G4$H4||10||16||8||None||[[Tetragonal trapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a5| | + | |{{FLD|a5|i|ade|cr|e5}} |
|[[Pentagonal pyramid]]||Unknown||&G5||6||10||6||None||Self-dual | |[[Pentagonal pyramid]]||Unknown||&G5||6||10||6||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a5| | + | |{{FLD|a5|i|ade|cr|e10}} |
|[[Pentagonal antiprism]]||Unknown||G5$H5||12||20||10||None||[[Pentagonal trapezohedron]] | |[[Pentagonal antiprism]]||Unknown||G5$H5||12||20||10||None||[[Pentagonal trapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a6| | + | |{{FLD|a6|i|ade|cr|e6}} |
|[[Hexagonal pyramid]]||Unknown||&G6||7||12||7||None||Self-dual | |[[Hexagonal pyramid]]||Unknown||&G6||7||12||7||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a6| | + | |{{FLD|a6|i|ade|cr|e12}} |
|[[Hexagonal antiprism]]||Unknown||G6$H6||16||28||14||None||[[Hexagonal trapezohedron]] | |[[Hexagonal antiprism]]||Unknown||G6$H6||16||28||14||None||[[Hexagonal trapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a8| | + | |{{FLD|a8|i|ade|cr|e8}} |
|[[Octagonal pyramid]]||Unknown||&G8||9||16||9||None||Self-dual | |[[Octagonal pyramid]]||Unknown||&G8||9||16||9||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a8| | + | |{{FLD|a8|i|ade|cr|e16}} |
|[[Octagonal antiprism]]||Unknown||G8$H8||20||36||18||None||[[Octagonal trapezohedron]] | |[[Octagonal antiprism]]||Unknown||G8$H8||20||36||18||None||[[Octagonal trapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a10| | + | |{{FLD|a10|i|ade|cr|e10}} |
|[[Decagonal pyramid]]||Unknown||&G10||11||20||11||None||Self-dual | |[[Decagonal pyramid]]||Unknown||&G10||11||20||11||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a10| | + | |{{FLD|a10|i|ade|cr|e20}} |
|[[Decagonal antiprism]]||Unknown||G10$H10||24||44||22||None||[[Decagonal trapezohedron]] | |[[Decagonal antiprism]]||Unknown||G10$H10||24||44||22||None||[[Decagonal trapezohedron]] | ||
|- | |- | ||
- | |{{FLD|left=e3| | + | |{{FLD|left=e3|dsev|aq|dsrmev|adl|e}} |
|[[Trigonal expanded antitrapezohedron]]||Unknown||Unknown||12||24||14||[[Endotrikis antiprism]]||[[Hexagonal semibipyramid]] | |[[Trigonal expanded antitrapezohedron]]||Unknown||Unknown||12||24||14||[[Endotrikis antiprism]]||[[Hexagonal semibipyramid]] | ||
|- | |- | ||
- | |{{FLD|left=e4| | + | |{{FLD|left=e4|dsev|aq|dsrmev|adl|e}} |
|[[Tetragonal expanded antitrapezohedron]]||Unknown||Unknown||16||32||18||[[Endotetrakis antiprism]]||[[Octagonal semibipyramid]] | |[[Tetragonal expanded antitrapezohedron]]||Unknown||Unknown||16||32||18||[[Endotetrakis antiprism]]||[[Octagonal semibipyramid]] | ||
|- | |- | ||
- | |{{FLD|left=e5| | + | |{{FLD|left=e5|dsev|aq|dsrmev|adl|e}} |
|[[Pentagonal expanded antitrapezohedron]]||Unknown||Unknown||20||40||22||[[Endopentakis antiprism]]||[[Decagonal semibipyramid]] | |[[Pentagonal expanded antitrapezohedron]]||Unknown||Unknown||20||40||22||[[Endopentakis antiprism]]||[[Decagonal semibipyramid]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|ate|i|a4|cr}} |
|[[Cubic snub]]||Unknown||Ko0||38||60||24||None||[[Pentagonal icositetrahedron]] | |[[Cubic snub]]||Unknown||Ko0||38||60||24||None||[[Pentagonal icositetrahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|ate|i|a5|cr}} |
|[[Dodecahedral snub]]||Unknown||Ki0||92||150||60||None||[[Pentagonal hexecontahedron]] | |[[Dodecahedral snub]]||Unknown||Ki0||92||150||60||None||[[Pentagonal hexecontahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a2|i|a4|cr}} |
|[[Cuboctahedral rectate]]||Unknown||Ko5||26||48||24||None||[[Deltoidal icositetrahedron]] | |[[Cuboctahedral rectate]]||Unknown||Ko5||26||48||24||None||[[Deltoidal icositetrahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|a2|i|a5|cr}} |
|[[Icosidodecahedral rectate]]||Unknown||Ki5||62||120||60||None||[[Deltoidal hexecontahedron]] | |[[Icosidodecahedral rectate]]||Unknown||Ki5||62||120||60||None||[[Deltoidal hexecontahedron]] | ||
|- | |- | ||
- | |{{FLD| | + | |{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}} |
|[[Cuboctahedral truncate]]||Unknown||Ko7||26||72||48||[[Cubic snub]]||[[Disdyakis dodecahedron]] | |[[Cuboctahedral truncate]]||Unknown||Ko7||26||72||48||[[Cubic snub]]||[[Disdyakis dodecahedron]] | ||
|- | |- | ||
- | |{{FLD| | + | |{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}} |
|[[Icosidodecahedral truncate]]||Unknown||Ki7||62||180||120||[[Dodecahedral snub]]||[[Disdyakis triacontahedron]] | |[[Icosidodecahedral truncate]]||Unknown||Ki7||62||180||120||[[Dodecahedral snub]]||[[Disdyakis triacontahedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|adr|edm|adl|e}} |
|[[Hexagonal semibipyramid]]||Unknown||Unknown||14||24||12||None||[[Trigonal expanded antitrapezohedron]] | |[[Hexagonal semibipyramid]]||Unknown||Unknown||14||24||12||None||[[Trigonal expanded antitrapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a4| | + | |{{FLD|a4|i|adr|edm|adl|e}} |
|[[Octagonal semibipyramid]]||Unknown||Unknown||18||32||16||None||[[Tetragonal expanded antitrapezohedron]] | |[[Octagonal semibipyramid]]||Unknown||Unknown||18||32||16||None||[[Tetragonal expanded antitrapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a5| | + | |{{FLD|a5|i|adr|edm|adl|e}} |
|[[Decagonal semibipyramid]]||Unknown||Unknown||22||40||20||None||[[Pentagonal expanded antitrapezohedron]] | |[[Decagonal semibipyramid]]||Unknown||Unknown||22||40||20||None||[[Pentagonal expanded antitrapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a3| | + | |{{FLD|a3|i|adr|dm|adl|i|asr|dse}} |
|[[Endotrikis antiprism]]||Unknown||Unknown||10||15||7||None||[[Trigonal trapezosemipyramid]] | |[[Endotrikis antiprism]]||Unknown||Unknown||10||15||7||None||[[Trigonal trapezosemipyramid]] | ||
|- | |- | ||
- | |{{FLD|a4| | + | |{{FLD|a4|i|adr|dm|adl|i|asr|dse}} |
|[[Endotetrakis antiprism]]||Unknown||Unknown||13||20||9||None||[[Tetragonal trapezosemipyramid]] | |[[Endotetrakis antiprism]]||Unknown||Unknown||13||20||9||None||[[Tetragonal trapezosemipyramid]] | ||
|- | |- | ||
- | |{{FLD|a5| | + | |{{FLD|a5|i|adr|dm|adl|i|asr|dse}} |
|[[Endopentakis antiprism]]||Unknown||Unknown||16||25||11||None||[[Pentagonal trapezosemipyramid]] | |[[Endopentakis antiprism]]||Unknown||Unknown||16||25||11||None||[[Pentagonal trapezosemipyramid]] | ||
|} | |} | ||
[[Category:Trishapes|$]] | [[Category:Trishapes|$]] |