List of polyhedra by facet layout (Meta, 12)
From Hi.gher. Space
(Difference between revisions)
m |
|||
Line 61: | Line 61: | ||
|[[Decagonal prism]]||Unknown||+G10||12||30||20||[[Pentagonal antiprism]]||[[Decagonal bipyramid]] | |[[Decagonal prism]]||Unknown||+G10||12||30||20||[[Pentagonal antiprism]]||[[Decagonal bipyramid]] | ||
|- | |- | ||
- | |{{FLD|a4|line| | + | |{{FLD|a4|line|adblend|cright|e4}} |
|[[Square pyramid]]||Unknown||&G4||5||8||5||None||Self-dual | |[[Square pyramid]]||Unknown||&G4||5||8||5||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a4|line| | + | |{{FLD|a4|line|adblend|cright|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|line| | + | |{{FLD|a5|line|adblend|cright|e5}} |
|[[Pentagonal pyramid]]||Unknown||&G5||6||10||6||None||Self-dual | |[[Pentagonal pyramid]]||Unknown||&G5||6||10||6||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a5|line| | + | |{{FLD|a5|line|adblend|cright|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|line| | + | |{{FLD|a6|line|adblend|cright|e6}} |
|[[Hexagonal pyramid]]||Unknown||&G6||7||12||7||None||Self-dual | |[[Hexagonal pyramid]]||Unknown||&G6||7||12||7||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a6|line| | + | |{{FLD|a6|line|adblend|cright|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|line| | + | |{{FLD|a8|line|adblend|cright|e8}} |
|[[Octagonal pyramid]]||Unknown||&G8||9||16||9||None||Self-dual | |[[Octagonal pyramid]]||Unknown||&G8||9||16||9||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a8|line| | + | |{{FLD|a8|line|adblend|cright|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|line| | + | |{{FLD|a10|line|adblend|cright|e10}} |
|[[Decagonal pyramid]]||Unknown||&G10||11||20||11||None||Self-dual | |[[Decagonal pyramid]]||Unknown||&G10||11||20||11||None||Self-dual | ||
|- | |- | ||
- | |{{FLD|a10|line| | + | |{{FLD|a10|line|adblend|cright|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|dbldiagerev|aquad|dbldiagrbarerev|adblleft|end}} |
|[[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|dbldiagerev|aquad|dbldiagrbarerev|adblleft|end}} |
|[[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|dbldiagerev|aquad|dbldiagrbarerev|adblleft|end}} |
|[[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|line| | + | |{{FLD|a3|line|atend|line|a4|cright}} |
|[[Cubic snub]]||Unknown||Ko0||38||60||24||None||[[Pentagonal icositetrahedron]] | |[[Cubic snub]]||Unknown||Ko0||38||60||24||None||[[Pentagonal icositetrahedron]] | ||
|- | |- | ||
- | |{{FLD|a3|line| | + | |{{FLD|a3|line|atend|line|a5|cright}} |
|[[Dodecahedral snub]]||Unknown||Ki0||92||150||60||None||[[Pentagonal hexecontahedron]] | |[[Dodecahedral snub]]||Unknown||Ki0||92||150||60||None||[[Pentagonal hexecontahedron]] | ||
|- | |- | ||
Line 112: | Line 112: | ||
|[[Icosidodecahedral rectate]]||Unknown||Ki5||62||120||60||None||[[Deltoidal hexecontahedron]] | |[[Icosidodecahedral rectate]]||Unknown||Ki5||62||120||60||None||[[Deltoidal hexecontahedron]] | ||
|- | |- | ||
- | |{{FLD| | + | |{{FLD|a2tright|tline|a3tbar|tline|a4tleft|cright}} |
|[[Cuboctahedral truncate]]||Unknown||Ko7||26||72||48||[[Cubic snub]]||[[Disdyakis dodecahedron]] | |[[Cuboctahedral truncate]]||Unknown||Ko7||26||72||48||[[Cubic snub]]||[[Disdyakis dodecahedron]] | ||
|- | |- | ||
- | |{{FLD| | + | |{{FLD|a2tright|tline|a3tbar|tline|a5tleft|cright}} |
|[[Icosidodecahedral truncate]]||Unknown||Ki7||62||180||120||[[Dodecahedral snub]]||[[Disdyakis triacontahedron]] | |[[Icosidodecahedral truncate]]||Unknown||Ki7||62||180||120||[[Dodecahedral snub]]||[[Disdyakis triacontahedron]] | ||
|- | |- | ||
- | |{{FLD|a3|line| | + | |{{FLD|a3|line|adblright|enddblbar|adblleft|end}} |
|[[Hexagonal semibipyramid]]||Unknown||Unknown||14||24||12||None||[[Trigonal expanded antitrapezohedron]] | |[[Hexagonal semibipyramid]]||Unknown||Unknown||14||24||12||None||[[Trigonal expanded antitrapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a4|line| | + | |{{FLD|a4|line|adblright|enddblbar|adblleft|end}} |
|[[Octagonal semibipyramid]]||Unknown||Unknown||18||32||16||None||[[Tetragonal expanded antitrapezohedron]] | |[[Octagonal semibipyramid]]||Unknown||Unknown||18||32||16||None||[[Tetragonal expanded antitrapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a5|line| | + | |{{FLD|a5|line|adblright|enddblbar|adblleft|end}} |
|[[Decagonal semibipyramid]]||Unknown||Unknown||22||40||20||None||[[Pentagonal expanded antitrapezohedron]] | |[[Decagonal semibipyramid]]||Unknown||Unknown||22||40||20||None||[[Pentagonal expanded antitrapezohedron]] | ||
|- | |- | ||
- | |{{FLD|a3|line| | + | |{{FLD|a3|line|adblright|dblbar|adblleft|line|adiagright|dbldiagend}} |
|[[Endotrikis antiprism]]||Unknown||Unknown||10||15||7||None||[[Trigonal trapezosemipyramid]] | |[[Endotrikis antiprism]]||Unknown||Unknown||10||15||7||None||[[Trigonal trapezosemipyramid]] | ||
|- | |- | ||
- | |{{FLD|a4|line| | + | |{{FLD|a4|line|adblright|dblbar|adblleft|line|adiagright|dbldiagend}} |
|[[Endotetrakis antiprism]]||Unknown||Unknown||13||20||9||None||[[Tetragonal trapezosemipyramid]] | |[[Endotetrakis antiprism]]||Unknown||Unknown||13||20||9||None||[[Tetragonal trapezosemipyramid]] | ||
|- | |- | ||
- | |{{FLD|a5|line| | + | |{{FLD|a5|line|adblright|dblbar|adblleft|line|adiagright|dbldiagend}} |
|[[Endopentakis antiprism]]||Unknown||Unknown||16||25||11||None||[[Pentagonal trapezosemipyramid]] | |[[Endopentakis antiprism]]||Unknown||Unknown||16||25||11||None||[[Pentagonal trapezosemipyramid]] | ||
|} | |} | ||
[[Category:Trishapes|$]] | [[Category:Trishapes|$]] |
Revision as of 22:45, 5 November 2009
Facet layout | Name | Petrie order | SSC2 | Faces | Edges | Vertices | Alternation | Dual | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Tetrahedron | 4,0 | Kt1 | 4 | 6 | 4 | None | Self-dual | ||||||||||
| Octahedron | 6,0 | Ko4 | 8 | 12 | 6 | None | Cube | ||||||||||
| Icosahedron | 10,2 | Ki4 | 20 | 30 | 12 | None | Dodecahedron | ||||||||||
| Cube | 6,2 | Ko1 | 6 | 12 | 8 | Tetrahedron | Octahedron | ||||||||||
| Dodecahedron | 10,10,0 | Ki1 | 12 | 30 | 20 | None | Icosahedron | ||||||||||
| Cuboctahedron | Unknown | Ko2 | 14 | 24 | 12 | None | Rhombic dodecahedron | ||||||||||
| Icosidodecahedron | Unknown | Ki2 | 32 | 60 | 30 | None | Rhombic triacontahedron | ||||||||||
| Triangular prism | Unknown | +G3 | 5 | 9 | 6 | None | Triangular bipyramid | ||||||||||
| Tetrahedral truncate | Unknown | Kt3 | 8 | 18 | 12 | None | Triakis tetrahedron | ||||||||||
| Cubic truncate | Unknown | Ko3 | 14 | 36 | 24 | None | Triakis octahedron | ||||||||||
| Dodecahedral truncate | Unknown | Ki3 | 32 | 90 | 60 | None | Triakis icosahedron | ||||||||||
| Octahedral truncate | Unknown | Ko6 | 14 | 36 | 24 | Icosahedron | Tetrakis hexahedron | ||||||||||
| Pentagonal prism | Unknown | +G5 | 7 | 15 | 10 | None | Pentagonal bipyramid | ||||||||||
| Icosahedral truncate | Unknown | Ki6 | 32 | 90 | 60 | None | Pentakis dodecahedron | ||||||||||
| Hexagonal prism | Unknown | +G6 | 8 | 18 | 12 | Octahedron | Hexagonal bipyramid | ||||||||||
| Octagonal prism | Unknown | +G8 | 10 | 24 | 16 | Square antiprism | Octagonal bipyramid | ||||||||||
| Decagonal prism | Unknown | +G10 | 12 | 30 | 20 | Pentagonal antiprism | Decagonal bipyramid | ||||||||||
| Square pyramid | Unknown | &G4 | 5 | 8 | 5 | None | Self-dual | ||||||||||
| Square antiprism | Unknown | G4$H4 | 10 | 16 | 8 | None | Tetragonal trapezohedron | ||||||||||
| Pentagonal pyramid | Unknown | &G5 | 6 | 10 | 6 | None | Self-dual | ||||||||||
| Pentagonal antiprism | Unknown | G5$H5 | 12 | 20 | 10 | None | Pentagonal trapezohedron | ||||||||||
| Hexagonal pyramid | Unknown | &G6 | 7 | 12 | 7 | None | Self-dual | ||||||||||
| Hexagonal antiprism | Unknown | G6$H6 | 16 | 28 | 14 | None | Hexagonal trapezohedron | ||||||||||
| Octagonal pyramid | Unknown | &G8 | 9 | 16 | 9 | None | Self-dual | ||||||||||
| Octagonal antiprism | Unknown | G8$H8 | 20 | 36 | 18 | None | Octagonal trapezohedron | ||||||||||
| Decagonal pyramid | Unknown | &G10 | 11 | 20 | 11 | None | Self-dual | ||||||||||
| Decagonal antiprism | Unknown | G10$H10 | 24 | 44 | 22 | None | Decagonal trapezohedron | ||||||||||
| Trigonal expanded antitrapezohedron | Unknown | Unknown | 12 | 24 | 14 | Endotrikis antiprism | Hexagonal semibipyramid | ||||||||||
| Tetragonal expanded antitrapezohedron | Unknown | Unknown | 16 | 32 | 18 | Endotetrakis antiprism | Octagonal semibipyramid | ||||||||||
| Pentagonal expanded antitrapezohedron | Unknown | Unknown | 20 | 40 | 22 | Endopentakis antiprism | Decagonal semibipyramid | ||||||||||
| Cubic snub | Unknown | Ko0 | 38 | 60 | 24 | None | Pentagonal icositetrahedron | ||||||||||
| Dodecahedral snub | Unknown | Ki0 | 92 | 150 | 60 | None | Pentagonal hexecontahedron | ||||||||||
| Cuboctahedral rectate | Unknown | Ko5 | 26 | 48 | 24 | None | Deltoidal icositetrahedron | ||||||||||
| Icosidodecahedral rectate | Unknown | Ki5 | 62 | 120 | 60 | None | Deltoidal hexecontahedron | ||||||||||
| Cuboctahedral truncate | Unknown | Ko7 | 26 | 72 | 48 | Cubic snub | Disdyakis dodecahedron | ||||||||||
| Icosidodecahedral truncate | Unknown | Ki7 | 62 | 180 | 120 | Dodecahedral snub | Disdyakis triacontahedron | ||||||||||
| Hexagonal semibipyramid | Unknown | Unknown | 14 | 24 | 12 | None | Trigonal expanded antitrapezohedron | ||||||||||
| Octagonal semibipyramid | Unknown | Unknown | 18 | 32 | 16 | None | Tetragonal expanded antitrapezohedron | ||||||||||
| Decagonal semibipyramid | Unknown | Unknown | 22 | 40 | 20 | None | Pentagonal expanded antitrapezohedron | ||||||||||
| Endotrikis antiprism | Unknown | Unknown | 10 | 15 | 7 | None | Trigonal trapezosemipyramid | ||||||||||
| Endotetrakis antiprism | Unknown | Unknown | 13 | 20 | 9 | None | Tetragonal trapezosemipyramid | ||||||||||
| Endopentakis antiprism | Unknown | Unknown | 16 | 25 | 11 | None | Pentagonal trapezosemipyramid |