List of polyhedra by facet layout (Meta, 12)

From Hi.gher. Space

(Difference between revisions)
(redoing table)
Line 1: Line 1:
-
{|style='width:100%;'
+
{|class='shapelist' style='width:100%;'
-
!style='width:8%;'|[[Facet layout]]
+
!colspan='3'|Parent
-
!style='width:16%;'|Name
+
!colspan='3' class='key'|Elements
-
!style='width:8%;'|[[Petrie order]]
+
!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:16%;'|Alternation
+
!style='width:10%;'|[[Facet layout]]
-
!style='width:16%;'|Dual
+
!style='width:20%;'|Name
 +
!style='width:8%;'|SSC2
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
|{{FLD|a3|er|e3}}
|{{FLD|a3|er|e3}}
-
|[[Tetrahedron]]||4,0||Kt1||4||6||4||None||Self-dual
+
|[[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]]||6,0||Ko4||8||12||6||None||[[Cube]]
+
|[[Octahedron]]||Ko4
-
|-
+
|- class='row1'
 +
|{{FLD|a5|er|e3}}
 +
|[[Dodecahedron]]||Ki1
 +
|12||30||20
|{{FLD|a3|er|e5}}
|{{FLD|a3|er|e5}}
-
|[[Icosahedron]]||10,2||Ki4||20||30||12||None||[[Dodecahedron]]
+
|[[Icosahedron]]||Ki4
-
|-
+
-
|{{FLD|a4|er|e3}}
+
-
|[[Cube]]||6,2||Ko1||6||12||8||[[Tetrahedron]]||[[Octahedron]]
+
-
|-
+
-
|{{FLD|a5|er|e3}}
+
-
|[[Dodecahedron]]||10,10,0||Ki1||12||30||20||None||[[Icosahedron]]
+
|-
|-
|{{FLD|a3|i|a4|cr}}
|{{FLD|a3|i|a4|cr}}
-
|[[Cuboctahedron]]||6,6,0||Ko2||14||24||12||None||[[Rhombic dodecahedron]]
+
|[[Cuboctahedron]]||Ko2||14||24||12||[[Rhombic dodecahedron]]
|-
|-
|{{FLD|a3|i|a5|cr}}
|{{FLD|a3|i|a5|cr}}
-
|[[Icosidodecahedron]]||Unknown||Ki2||32||60||30||None||[[Rhombic triacontahedron]]
+
|[[Icosidodecahedron]]||Ki2||32||60||30||[[Rhombic triacontahedron]]
|-
|-
|{{FLD|a3|i|a2|er}}
|{{FLD|a3|i|a2|er}}
-
|[[Triangular prism]]||Unknown||+G3||5||9||6||None||[[Triangular bipyramid]]
+
|[[Triangular prism]]||+G3||5||9||6||[[Triangular bipyramid]]
|-
|-
|{{FLD|a3|i|a3|er}}
|{{FLD|a3|i|a3|er}}
-
|[[Tetrahedral truncate]]||Unknown||Kt3||8||18||12||None||[[Triakis tetrahedron]]
+
|[[Tetrahedral truncate]]||Kt3||8||18||12||[[Triakis tetrahedron]]
|-
|-
|{{FLD|a3|i|a4|er}}
|{{FLD|a3|i|a4|er}}
-
|[[Cubic truncate]]||Unknown||Ko3||14||36||24||None||[[Triakis octahedron]]
+
|[[Cubic truncate]]||Ko3||14||36||24||[[Triakis octahedron]]
|-
|-
|{{FLD|a3|i|a5|er}}
|{{FLD|a3|i|a5|er}}
-
|[[Dodecahedral truncate]]||Unknown||Ki3||32||90||60||None||[[Triakis icosahedron]]
+
|[[Dodecahedral truncate]]||Ki3||32||90||60||[[Triakis icosahedron]]
|-
|-
|{{FLD|a4|i|a3|er}}
|{{FLD|a4|i|a3|er}}
-
|[[Octahedral truncate]]||Unknown||Ko6||14||36||24||[[Icosahedron]]||[[Tetrakis hexahedron]]
+
|[[Octahedral truncate]]||Ko6||14||36||24||[[Tetrakis hexahedron]]
|-
|-
|{{FLD|a5|i|a2|er}}
|{{FLD|a5|i|a2|er}}
-
|[[Pentagonal prism]]||Unknown||+G5||7||15||10||None||[[Pentagonal bipyramid]]
+
|[[Pentagonal prism]]||+G5||7||15||10||[[Pentagonal bipyramid]]
|-
|-
|{{FLD|a5|i|a3|er}}
|{{FLD|a5|i|a3|er}}
-
|[[Icosahedral truncate]]||Unknown||Ki6||32||90||60||None||[[Pentakis dodecahedron]]
+
|[[Icosahedral truncate]]||Ki6||32||90||60||[[Pentakis dodecahedron]]
|-
|-
|{{FLD|a6|i|a2|er}}
|{{FLD|a6|i|a2|er}}
-
|[[Hexagonal prism]]||Unknown||+G6||8||18||12||[[Octahedron]]||[[Hexagonal bipyramid]]
+
|[[Hexagonal prism]]||+G6||8||18||12||[[Hexagonal bipyramid]]
|-
|-
|{{FLD|a8|i|a2|er}}
|{{FLD|a8|i|a2|er}}
-
|[[Octagonal prism]]||Unknown||+G8||10||24||16||[[Square antiprism]]||[[Octagonal bipyramid]]
+
|[[Octagonal prism]]||+G8||10||24||16||[[Octagonal bipyramid]]
|-
|-
|{{FLD|a10|i|a2|er}}
|{{FLD|a10|i|a2|er}}
-
|[[Decagonal prism]]||Unknown||+G10||12||30||20||[[Pentagonal antiprism]]||[[Decagonal bipyramid]]
+
|[[Decagonal prism]]||+G10||12||30||20||[[Decagonal bipyramid]]
|-
|-
|{{FLD|a4|i|ade|cr|e4}}
|{{FLD|a4|i|ade|cr|e4}}
-
|[[Square pyramid]]||Unknown||&G4||5||8||5||None||Self-dual
+
|[[Square pyramid]]||&G4||5||8||5||Self-dual
|-
|-
|{{FLD|a4|i|ade|cr|e8}}
|{{FLD|a4|i|ade|cr|e8}}
-
|[[Square antiprism]]||Unknown||G4$H4||10||16||8||None||[[Tetragonal trapezohedron]]
+
|[[Square antiprism]]||G4$H4||10||16||8||[[Tetragonal trapezohedron]]
|-
|-
|{{FLD|a5|i|ade|cr|e5}}
|{{FLD|a5|i|ade|cr|e5}}
-
|[[Pentagonal pyramid]]||Unknown||&G5||6||10||6||None||Self-dual
+
|[[Pentagonal pyramid]]||&G5||6||10||6||Self-dual
|-
|-
|{{FLD|a5|i|ade|cr|e10}}
|{{FLD|a5|i|ade|cr|e10}}
-
|[[Pentagonal antiprism]]||Unknown||G5$H5||12||20||10||None||[[Pentagonal trapezohedron]]
+
|[[Pentagonal antiprism]]||G5$H5||12||20||10||[[Pentagonal trapezohedron]]
|-
|-
|{{FLD|a6|i|ade|cr|e6}}
|{{FLD|a6|i|ade|cr|e6}}
-
|[[Hexagonal pyramid]]||Unknown||&G6||7||12||7||None||Self-dual
+
|[[Hexagonal pyramid]]||&G6||7||12||7||Self-dual
|-
|-
|{{FLD|a6|i|ade|cr|e12}}
|{{FLD|a6|i|ade|cr|e12}}
-
|[[Hexagonal antiprism]]||Unknown||G6$H6||16||28||14||None||[[Hexagonal trapezohedron]]
+
|[[Hexagonal antiprism]]||G6$H6||16||28||14||[[Hexagonal trapezohedron]]
|-
|-
|{{FLD|a8|i|ade|cr|e8}}
|{{FLD|a8|i|ade|cr|e8}}
-
|[[Octagonal pyramid]]||Unknown||&G8||9||16||9||None||Self-dual
+
|[[Octagonal pyramid]]||&G8||9||16||9||Self-dual
|-
|-
|{{FLD|a8|i|ade|cr|e16}}
|{{FLD|a8|i|ade|cr|e16}}
-
|[[Octagonal antiprism]]||Unknown||G8$H8||20||36||18||None||[[Octagonal trapezohedron]]
+
|[[Octagonal antiprism]]||G8$H8||20||36||18||[[Octagonal trapezohedron]]
|-
|-
|{{FLD|a10|i|ade|cr|e10}}
|{{FLD|a10|i|ade|cr|e10}}
-
|[[Decagonal pyramid]]||Unknown||&G10||11||20||11||None||Self-dual
+
|[[Decagonal pyramid]]||&G10||11||20||11||Self-dual
|-
|-
|{{FLD|a10|i|ade|cr|e20}}
|{{FLD|a10|i|ade|cr|e20}}
-
|[[Decagonal antiprism]]||Unknown||G10$H10||24||44||22||None||[[Decagonal trapezohedron]]
+
|[[Decagonal antiprism]]||G10$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]]||Unknown||Unknown||12||24||14||[[Endotrikis antiprism]]||[[Triangular orthobicupola]]
+
|[[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]]||Unknown||Unknown||16||32||18||[[Endotetrakis antiprism]]||[[Square orthobicupola]]
+
|[[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]]||Unknown||Unknown||20||40||22||[[Endopentakis antiprism]]||[[Pentagonal orthobicupola]]
+
|[[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]]||Unknown||Ko0||38||60||24||None||[[Pentagonal icositetrahedron]]
+
|[[Cubic snub]]||Ko0||38||60||24||[[Pentagonal icositetrahedron]]
|-
|-
|{{FLD|a3|i|ate|i|a5|cr}}
|{{FLD|a3|i|ate|i|a5|cr}}
-
|[[Dodecahedral snub]]||Unknown||Ki0||92||150||60||None||[[Pentagonal hexecontahedron]]
+
|[[Dodecahedral snub]]||Ki0||92||150||60||[[Pentagonal hexecontahedron]]
|-
|-
|{{FLD|a3|i|a2|i|a4|cr}}
|{{FLD|a3|i|a2|i|a4|cr}}
-
|[[Cuboctahedral rectate]]||Unknown||Ko5||26||48||24||None||[[Deltoidal icositetrahedron]]
+
|[[Cuboctahedral rectate]]||Ko5||26||48||24||[[Deltoidal icositetrahedron]]
|-
|-
|{{FLD|a3|i|a2|i|a5|cr}}
|{{FLD|a3|i|a2|i|a5|cr}}
-
|[[Icosidodecahedral rectate]]||Unknown||Ki5||62||120||60||None||[[Deltoidal hexecontahedron]]
+
|[[Icosidodecahedral rectate]]||Ki5||62||120||60||[[Deltoidal hexecontahedron]]
|-
|-
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}}
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}}
-
|[[Cuboctahedral truncate]]||Unknown||Ko7||26||72||48||[[Cubic snub]]||[[Disdyakis dodecahedron]]
+
|[[Cuboctahedral truncate]]||Ko7||26||72||48||[[Disdyakis dodecahedron]]
|-
|-
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}}
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}}
-
|[[Icosidodecahedral truncate]]||Unknown||Ki7||62||180||120||[[Dodecahedral snub]]||[[Disdyakis triacontahedron]]
+
|[[Icosidodecahedral truncate]]||Ki7||62||180||120||[[Disdyakis triacontahedron]]
|-
|-
|{{FLD|a3|i|adr|edm|adl|er}}
|{{FLD|a3|i|adr|edm|adl|er}}
-
|[[Triangular orthobicupola]]||Unknown||Unknown||14||24||12||None||[[Trigonal expanded antitrapezohedron]]
+
|[[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]]||Unknown||Unknown||18||32||16||None||[[Tetragonal expanded antitrapezohedron]]
+
|[[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]]||Unknown||Unknown||22||40||20||None||[[Pentagonal expanded antitrapezohedron]]
+
|[[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]]||Unknown||Unknown||10||15||7||None||[[Trigonal trapezosemipyramid]]
+
|[[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]]||Unknown||Unknown||13||20||9||None||[[Tetragonal trapezosemipyramid]]
+
|[[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]]||Unknown||Unknown||16||25||11||None||[[Pentagonal trapezosemipyramid]]
+
|[[Endopentakis antiprism]]||Unknown||16||25||11||[[Pentagonal trapezosemipyramid]]
|}
|}
[[Category:Trishapes|$]]
[[Category:Trishapes|$]]

Revision as of 22:19, 10 January 2012

Parent Elements Dual
Facet layout Name SSC2 Faces Edges Vertices Facet layout Name SSC2
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
TetrahedronKt1 464 Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
CubeKo1 6128
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
OctahedronKo4
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
DodecahedronKi1 123020
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
IcosahedronKi4
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
CuboctahedronKo2142412Rhombic dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
IcosidodecahedronKi2326030Rhombic triacontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Triangular prism+G3596Triangular bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Tetrahedral truncateKt381812Triakis tetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cubic truncateKo3143624Triakis octahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Dodecahedral truncateKi3329060Triakis icosahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octahedral truncateKo6143624Tetrakis hexahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal prism+G571510Pentagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosahedral truncateKi6329060Pentakis dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal prism+G681812Hexagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal prism+G8102416Octagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal prism+G10123020Decagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square pyramid&G4585Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square antiprismG4$H410168Tetragonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal pyramid&G56106Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal antiprismG5$H5122010Pentagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal pyramid&G67127Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal antiprismG6$H6162814Hexagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal pyramid&G89169Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal antiprismG8$H8203618Octagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal pyramid&G10112011Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal antiprismG10$H10244422Decagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Trigonal expanded antitrapezohedronUnknown122414Triangular orthobicupola
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Tetragonal expanded antitrapezohedronUnknown163218Square orthobicupola
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal expanded antitrapezohedronUnknown204022Pentagonal orthobicupola
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cubic snubKo0386024Pentagonal icositetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Dodecahedral snubKi09215060Pentagonal hexecontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cuboctahedral rectateKo5264824Deltoidal icositetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosidodecahedral rectateKi56212060Deltoidal hexecontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cuboctahedral truncateKo7267248Disdyakis dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosidodecahedral truncateKi762180120Disdyakis triacontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Triangular orthobicupolaUnknown142412Trigonal expanded antitrapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square orthobicupolaUnknown183216Tetragonal expanded antitrapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal orthobicupolaUnknown224020Pentagonal expanded antitrapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endotrikis antiprismUnknown10157Trigonal trapezosemipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endotetrakis antiprismUnknown13209Tetragonal trapezosemipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endopentakis antiprismUnknown162511Pentagonal trapezosemipyramid