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|end|e3}}
+
|{{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|end|e4}}
+
|{{FLD|a3|e|e4}}
|[[Octahedron]]||6,0||Ko4||8||12||6||None||[[Cube]]
|[[Octahedron]]||6,0||Ko4||8||12||6||None||[[Cube]]
|-
|-
-
|{{FLD|a3|end|e5}}
+
|{{FLD|a3|e|e5}}
|[[Icosahedron]]||10,2||Ki4||20||30||12||None||[[Dodecahedron]]
|[[Icosahedron]]||10,2||Ki4||20||30||12||None||[[Dodecahedron]]
|-
|-
-
|{{FLD|a4|end|e3}}
+
|{{FLD|a4|e|e3}}
|[[Cube]]||6,2||Ko1||6||12||8||[[Tetrahedron]]||[[Octahedron]]
|[[Cube]]||6,2||Ko1||6||12||8||[[Tetrahedron]]||[[Octahedron]]
|-
|-
-
|{{FLD|a5|end|e3}}
+
|{{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|line|a4|cright}}
+
|{{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|line|a5|cright}}
+
|{{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|line|a2|end}}
+
|{{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|line|a3|end}}
+
|{{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|line|a4|end}}
+
|{{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|line|a5|end}}
+
|{{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|line|a3|end}}
+
|{{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|line|a2|end}}
+
|{{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|line|a3|end}}
+
|{{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|line|a2|end}}
+
|{{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|line|a2|end}}
+
|{{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|line|a2|end}}
+
|{{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|line|adblend|cright|e4}}
+
|{{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|line|adblend|cright|e8}}
+
|{{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|line|adblend|cright|e5}}
+
|{{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|line|adblend|cright|e10}}
+
|{{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|line|adblend|cright|e6}}
+
|{{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|line|adblend|cright|e12}}
+
|{{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|line|adblend|cright|e8}}
+
|{{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|line|adblend|cright|e16}}
+
|{{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|line|adblend|cright|e10}}
+
|{{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|line|adblend|cright|e20}}
+
|{{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|dbldiagerev|aquad|dbldiagrbarerev|adblleft|end}}
+
|{{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|dbldiagerev|aquad|dbldiagrbarerev|adblleft|end}}
+
|{{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|dbldiagerev|aquad|dbldiagrbarerev|adblleft|end}}
+
|{{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|line|atend|line|a4|cright}}
+
|{{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|line|atend|line|a5|cright}}
+
|{{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|line|a2|line|a4|cright}}
+
|{{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|line|a2|line|a5|cright}}
+
|{{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|a2tright|tline|a3tbar|tline|a4tleft|cright}}
+
|{{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|a2tright|tline|a3tbar|tline|a5tleft|cright}}
+
|{{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|line|adblright|enddblbar|adblleft|end}}
+
|{{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|line|adblright|enddblbar|adblleft|end}}
+
|{{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|line|adblright|enddblbar|adblleft|end}}
+
|{{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|line|adblright|dblbar|adblleft|line|adiagright|dbldiagend}}
+
|{{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|line|adblright|dblbar|adblleft|line|adiagright|dbldiagend}}
+
|{{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|line|adblright|dblbar|adblleft|line|adiagright|dbldiagend}}
+
|{{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|$]]
[[Category:Trishapes|$]]

Revision as of 18:08, 19 February 2011

Facet layout Name Petrie order SSC2 Faces Edges Vertices Alternation Dual
(image) (image) No such file (image) (image) (image) (image) (image) (image) (image)
Tetrahedron4,0Kt1464NoneSelf-dual
(image) (image) No such file (image) (image) (image) (image) (image) (image) (image)
Octahedron6,0Ko48126NoneCube
(image) (image) No such file (image) (image) (image) (image) (image) (image) (image)
Icosahedron10,2Ki4203012NoneDodecahedron
(image) (image) No such file (image) (image) (image) (image) (image) (image) (image)
Cube6,2Ko16128TetrahedronOctahedron
(image) (image) No such file (image) (image) (image) (image) (image) (image) (image)
Dodecahedron10,10,0Ki1123020NoneIcosahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
CuboctahedronUnknownKo2142412NoneRhombic dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
IcosidodecahedronUnknownKi2326030NoneRhombic triacontahedron
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Triangular prismUnknown+G3596NoneTriangular bipyramid
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Tetrahedral truncateUnknownKt381812NoneTriakis tetrahedron
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Cubic truncateUnknownKo3143624NoneTriakis octahedron
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Dodecahedral truncateUnknownKi3329060NoneTriakis icosahedron
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Octahedral truncateUnknownKo6143624IcosahedronTetrakis hexahedron
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Pentagonal prismUnknown+G571510NonePentagonal bipyramid
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Icosahedral truncateUnknownKi6329060NonePentakis dodecahedron
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Hexagonal prismUnknown+G681812OctahedronHexagonal bipyramid
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Octagonal prismUnknown+G8102416Square antiprismOctagonal bipyramid
(image) (image) (image) (image) No such file (image) (image) (image) (image) (image)
Decagonal prismUnknown+G10123020Pentagonal antiprismDecagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square pyramidUnknown&G4585NoneSelf-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square antiprismUnknownG4$H410168NoneTetragonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal pyramidUnknown&G56106NoneSelf-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal antiprismUnknownG5$H5122010NonePentagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal pyramidUnknown&G67127NoneSelf-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal antiprismUnknownG6$H6162814NoneHexagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal pyramidUnknown&G89169NoneSelf-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal antiprismUnknownG8$H8203618NoneOctagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal pyramidUnknown&G10112011NoneSelf-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal antiprismUnknownG10$H10244422NoneDecagonal trapezohedron
(image) No such file (image) No such file (image) No such file (image) (image) (image) (image)
Trigonal expanded antitrapezohedronUnknownUnknown122414Endotrikis antiprismHexagonal semibipyramid
(image) No such file (image) No such file (image) No such file (image) (image) (image) (image)
Tetragonal expanded antitrapezohedronUnknownUnknown163218Endotetrakis antiprismOctagonal semibipyramid
(image) No such file (image) No such file (image) No such file (image) (image) (image) (image)
Pentagonal expanded antitrapezohedronUnknownUnknown204022Endopentakis antiprismDecagonal semibipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cubic snubUnknownKo0386024NonePentagonal icositetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Dodecahedral snubUnknownKi09215060NonePentagonal hexecontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cuboctahedral rectateUnknownKo5264824NoneDeltoidal icositetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosidodecahedral rectateUnknownKi56212060NoneDeltoidal hexecontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cuboctahedral truncateUnknownKo7267248Cubic snubDisdyakis dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosidodecahedral truncateUnknownKi762180120Dodecahedral snubDisdyakis triacontahedron
(image) (image) (image) (image) (image) (image) No such file (image) (image) (image)
Hexagonal semibipyramidUnknownUnknown142412NoneTrigonal expanded antitrapezohedron
(image) (image) (image) (image) (image) (image) No such file (image) (image) (image)
Octagonal semibipyramidUnknownUnknown183216NoneTetragonal expanded antitrapezohedron
(image) (image) (image) (image) (image) (image) No such file (image) (image) (image)
Decagonal semibipyramidUnknownUnknown224020NonePentagonal expanded antitrapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) No such file (image)
Endotrikis antiprismUnknownUnknown10157NoneTrigonal trapezosemipyramid
(image) (image) (image) (image) (image) (image) (image) (image) No such file (image)
Endotetrakis antiprismUnknownUnknown13209NoneTetragonal trapezosemipyramid
(image) (image) (image) (image) (image) (image) (image) (image) No such file (image)
Endopentakis antiprismUnknownUnknown162511NonePentagonal trapezosemipyramid