List of polyhedra by facet layout (Meta, 12)

From Hi.gher. Space

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|[[Icosahedron]]||Ki4
|[[Icosahedron]]||Ki4
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row2'
|{{FLD|a3|i|a4|cr}}
|{{FLD|a3|i|a4|cr}}
-
|[[Cuboctahedron]]||Ko2||14||24||12||[[Rhombic dodecahedron]]
+
|[[Cuboctahedron]]||Ko2
-
|-
+
|14||24||12
 +
|[[Rhombic dodecahedron]]
 +
|- class='row1'
|{{FLD|a3|i|a5|cr}}
|{{FLD|a3|i|a5|cr}}
-
|[[Icosidodecahedron]]||Ki2||32||60||30||[[Rhombic triacontahedron]]
+
|[[Icosidodecahedron]]||Ki2
-
|-
+
|32||60||30
-
|{{FLD|a3|i|a2|er}}
+
|[[Rhombic triacontahedron]]
-
|[[Triangular prism]]||+G3||5||9||6||[[Triangular bipyramid]]
+
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row2'
|{{FLD|a3|i|a3|er}}
|{{FLD|a3|i|a3|er}}
-
|[[Tetrahedral truncate]]||Kt3||8||18||12||[[Triakis tetrahedron]]
+
|[[Tetrahedral truncate]]||Kt3
-
|-
+
|8||18||12
 +
|[[Triakis tetrahedron]]
 +
|- class='row1'
|{{FLD|a3|i|a4|er}}
|{{FLD|a3|i|a4|er}}
-
|[[Cubic truncate]]||Ko3||14||36||24||[[Triakis octahedron]]
+
|[[Cubic truncate]]||Ko3
-
|-
+
|14||36||24
 +
|[[Triakis octahedron]]
 +
|- class='row2'
|{{FLD|a3|i|a5|er}}
|{{FLD|a3|i|a5|er}}
-
|[[Dodecahedral truncate]]||Ki3||32||90||60||[[Triakis icosahedron]]
+
|[[Dodecahedral truncate]]||Ki3
-
|-
+
|32||90||60
 +
|[[Triakis icosahedron]]
 +
|- class='row1'
|{{FLD|a4|i|a3|er}}
|{{FLD|a4|i|a3|er}}
-
|[[Octahedral truncate]]||Ko6||14||36||24||[[Tetrakis hexahedron]]
+
|[[Octahedral truncate]]||Ko6
 +
|14||36||24
 +
|[[Tetrakis hexahedron]]
 +
|- class='row2'
 +
|{{FLD|a5|i|a3|er}}
 +
|[[Icosahedral truncate]]||Ki6
 +
|32||90||60
 +
|[[Pentakis dodecahedron]]
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
 +
|{{FLD|a3|i|a2|er}}
 +
|[[Triangular prism]]||+G3
 +
|5||9||6
 +
|[[Triangular bipyramid]]
 +
|- class='row2'
|{{FLD|a5|i|a2|er}}
|{{FLD|a5|i|a2|er}}
-
|[[Pentagonal prism]]||+G5||7||15||10||[[Pentagonal bipyramid]]
+
|[[Pentagonal prism]]||+G5
-
|-
+
|7||15||10
-
|{{FLD|a5|i|a3|er}}
+
|[[Pentagonal bipyramid]]
-
|[[Icosahedral truncate]]||Ki6||32||90||60||[[Pentakis dodecahedron]]
+
|- class='row1'
-
|-
+
|{{FLD|a6|i|a2|er}}
|{{FLD|a6|i|a2|er}}
-
|[[Hexagonal prism]]||+G6||8||18||12||[[Hexagonal bipyramid]]
+
|[[Hexagonal prism]]||+G6
-
|-
+
|8||18||12
 +
|[[Hexagonal bipyramid]]
 +
|- class='row2'
|{{FLD|a8|i|a2|er}}
|{{FLD|a8|i|a2|er}}
-
|[[Octagonal prism]]||+G8||10||24||16||[[Octagonal bipyramid]]
+
|[[Octagonal prism]]||+G8
-
|-
+
|10||24||16
 +
|[[Octagonal bipyramid]]
 +
|- class='row1'
|{{FLD|a10|i|a2|er}}
|{{FLD|a10|i|a2|er}}
-
|[[Decagonal prism]]||+G10||12||30||20||[[Decagonal bipyramid]]
+
|[[Decagonal prism]]||+G10
 +
|12||30||20
 +
|[[Decagonal bipyramid]]
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row2'
|{{FLD|a4|i|ade|cr|e4}}
|{{FLD|a4|i|ade|cr|e4}}
-
|[[Square pyramid]]||&G4||5||8||5||Self-dual
+
|[[Square pyramid]]||&G4
 +
|5||8||5
 +
|Self-dual
 +
|- class='row1'
 +
|{{FLD|a5|i|ade|cr|e5}}
 +
|[[Pentagonal pyramid]]||&G5
 +
|6||10||6
 +
|Self-dual
 +
|- class='row2'
 +
|{{FLD|a6|i|ade|cr|e6}}
 +
|[[Hexagonal pyramid]]||&G6
 +
|7||12||7
 +
|Self-dual
 +
|- class='row1'
 +
|{{FLD|a8|i|ade|cr|e8}}
 +
|[[Octagonal pyramid]]||&G8
 +
|9||16||9
 +
|Self-dual
 +
|- class='row2'
 +
|{{FLD|a10|i|ade|cr|e10}}
 +
|[[Decagonal pyramid]]||&G10
 +
|11||20||11
 +
|Self-dual
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
|{{FLD|a4|i|ade|cr|e8}}
|{{FLD|a4|i|ade|cr|e8}}
-
|[[Square antiprism]]||G4$H4||10||16||8||[[Tetragonal trapezohedron]]
+
|[[Square antiprism]]||G4$H4
-
|-
+
|10||16||8
-
|{{FLD|a5|i|ade|cr|e5}}
+
|[[Tetragonal trapezohedron]]
-
|[[Pentagonal pyramid]]||&G5||6||10||6||Self-dual
+
|- class='row2'
-
|-
+
|{{FLD|a5|i|ade|cr|e10}}
|{{FLD|a5|i|ade|cr|e10}}
-
|[[Pentagonal antiprism]]||G5$H5||12||20||10||[[Pentagonal trapezohedron]]
+
|[[Pentagonal antiprism]]||G5$H5
-
|-
+
|12||20||10
-
|{{FLD|a6|i|ade|cr|e6}}
+
|[[Pentagonal trapezohedron]]
-
|[[Hexagonal pyramid]]||&G6||7||12||7||Self-dual
+
|- class='row1'
-
|-
+
|{{FLD|a6|i|ade|cr|e12}}
|{{FLD|a6|i|ade|cr|e12}}
-
|[[Hexagonal antiprism]]||G6$H6||16||28||14||[[Hexagonal trapezohedron]]
+
|[[Hexagonal antiprism]]||G6$H6
-
|-
+
|16||28||14
-
|{{FLD|a8|i|ade|cr|e8}}
+
|[[Hexagonal trapezohedron]]
-
|[[Octagonal pyramid]]||&G8||9||16||9||Self-dual
+
|- class='row2'
-
|-
+
|{{FLD|a8|i|ade|cr|e16}}
|{{FLD|a8|i|ade|cr|e16}}
-
|[[Octagonal antiprism]]||G8$H8||20||36||18||[[Octagonal trapezohedron]]
+
|[[Octagonal antiprism]]||G8$H8
-
|-
+
|20||36||18
-
|{{FLD|a10|i|ade|cr|e10}}
+
|[[Octagonal trapezohedron]]
-
|[[Decagonal pyramid]]||&G10||11||20||11||Self-dual
+
|- class='row1'
-
|-
+
|{{FLD|a10|i|ade|cr|e20}}
|{{FLD|a10|i|ade|cr|e20}}
-
|[[Decagonal antiprism]]||G10$H10||24||44||22||[[Decagonal trapezohedron]]
+
|[[Decagonal antiprism]]||G10$H10
 +
|24||44||22
 +
|[[Decagonal trapezohedron]]
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row2'
|{{FLD|left=e3|dsel|aq|dsrmel|adl|er}}
|{{FLD|left=e3|dsel|aq|dsrmel|adl|er}}
-
|[[Trigonal expanded antitrapezohedron]]||Unknown||12||24||14||[[Triangular orthobicupola]]
+
|[[Trigonal expanded antitrapezohedron]]||Unknown
-
|-
+
|12||24||14
 +
|{{FLD|a3|i|adr|edm|adl|er}}
 +
|[[Triangular orthobicupola]]||Unknown
 +
|- class='row1'
|{{FLD|left=e4|dsel|aq|dsrmel|adl|er}}
|{{FLD|left=e4|dsel|aq|dsrmel|adl|er}}
-
|[[Tetragonal expanded antitrapezohedron]]||Unknown||16||32||18||[[Square orthobicupola]]
+
|[[Tetragonal expanded antitrapezohedron]]||Unknown
-
|-
+
|16||32||18
 +
|{{FLD|a4|i|adr|edm|adl|er}}
 +
|[[Square orthobicupola]]||Unknown
 +
|- class='row2'
|{{FLD|left=e5|dsel|aq|dsrmel|adl|er}}
|{{FLD|left=e5|dsel|aq|dsrmel|adl|er}}
-
|[[Pentagonal expanded antitrapezohedron]]||Unknown||20||40||22||[[Pentagonal orthobicupola]]
+
|[[Pentagonal expanded antitrapezohedron]]||Unknown
 +
|20||40||22
 +
|{{FLD|a5|i|adr|edm|adl|er}}
 +
|[[Pentagonal orthobicupola]]||Unknown
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
|{{FLD|a3|i|ate|i|a4|cr}}
|{{FLD|a3|i|ate|i|a4|cr}}
-
|[[Cubic snub]]||Ko0||38||60||24||[[Pentagonal icositetrahedron]]
+
|[[Cubic snub]]||Ko0
-
|-
+
|38||60||24
 +
|[[Pentagonal icositetrahedron]]
 +
|- class='row2'
|{{FLD|a3|i|ate|i|a5|cr}}
|{{FLD|a3|i|ate|i|a5|cr}}
-
|[[Dodecahedral snub]]||Ki0||92||150||60||[[Pentagonal hexecontahedron]]
+
|[[Dodecahedral snub]]||Ki0
 +
|92||150||60
 +
|[[Pentagonal hexecontahedron]]
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
|{{FLD|a3|i|a2|i|a4|cr}}
|{{FLD|a3|i|a2|i|a4|cr}}
-
|[[Cuboctahedral rectate]]||Ko5||26||48||24||[[Deltoidal icositetrahedron]]
+
|[[Cuboctahedral rectate]]||Ko5
-
|-
+
|26||48||24
 +
|[[Deltoidal icositetrahedron]]
 +
|- class='row2'
|{{FLD|a3|i|a2|i|a5|cr}}
|{{FLD|a3|i|a2|i|a5|cr}}
-
|[[Icosidodecahedral rectate]]||Ki5||62||120||60||[[Deltoidal hexecontahedron]]
+
|[[Icosidodecahedral rectate]]||Ki5
 +
|62||120||60
 +
|[[Deltoidal hexecontahedron]]
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}}
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}}
-
|[[Cuboctahedral truncate]]||Ko7||26||72||48||[[Disdyakis dodecahedron]]
+
|[[Cuboctahedral truncate]]||Ko7
-
|-
+
|26||72||48
 +
|[[Disdyakis dodecahedron]]
 +
|- class='row2'
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}}
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}}
-
|[[Icosidodecahedral truncate]]||Ki7||62||180||120||[[Disdyakis triacontahedron]]
+
|[[Icosidodecahedral truncate]]||Ki7
-
|-
+
|62||180||120
-
|{{FLD|a3|i|adr|edm|adl|er}}
+
|[[Disdyakis triacontahedron]]
-
|[[Triangular orthobicupola]]||Unknown||14||24||12||[[Trigonal expanded antitrapezohedron]]
+
-
|-
+
-
|{{FLD|a4|i|adr|edm|adl|er}}
+
-
|[[Square orthobicupola]]||Unknown||18||32||16||[[Tetragonal expanded antitrapezohedron]]
+
-
|-
+
-
|{{FLD|a5|i|adr|edm|adl|er}}
+
-
|[[Pentagonal orthobicupola]]||Unknown||22||40||20||[[Pentagonal expanded antitrapezohedron]]
+
|-
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
|{{FLD|a3|i|adr|dm|adl|i|asr|dser}}
|{{FLD|a3|i|adr|dm|adl|i|asr|dser}}
-
|[[Endotrikis antiprism]]||Unknown||10||15||7||[[Trigonal trapezosemipyramid]]
+
|[[Endotrikis antiprism]]||Unknown
-
|-
+
|10||15||7
 +
|[[Trigonal trapezosemipyramid]]
 +
|- class='row2'
|{{FLD|a4|i|adr|dm|adl|i|asr|dser}}
|{{FLD|a4|i|adr|dm|adl|i|asr|dser}}
-
|[[Endotetrakis antiprism]]||Unknown||13||20||9||[[Tetragonal trapezosemipyramid]]
+
|[[Endotetrakis antiprism]]||Unknown
-
|-
+
|13||20||9
 +
|[[Tetragonal trapezosemipyramid]]
 +
|- class='row1'
|{{FLD|a5|i|adr|dm|adl|i|asr|dser}}
|{{FLD|a5|i|adr|dm|adl|i|asr|dser}}
-
|[[Endopentakis antiprism]]||Unknown||16||25||11||[[Pentagonal trapezosemipyramid]]
+
|[[Endopentakis antiprism]]||Unknown
 +
|16||25||11
 +
|[[Pentagonal trapezosemipyramid]]
|}
|}
[[Category:Trishapes|$]]
[[Category:Trishapes|$]]

Revision as of 22:37, 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)
CuboctahedronKo2 142412 Rhombic dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
IcosidodecahedronKi2 326030 Rhombic triacontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Tetrahedral truncateKt3 81812 Triakis tetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cubic truncateKo3 143624 Triakis octahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Dodecahedral truncateKi3 329060 Triakis icosahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octahedral truncateKo6 143624 Tetrakis hexahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosahedral truncateKi6 329060 Pentakis dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Triangular prism+G3 596 Triangular bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal prism+G5 71510 Pentagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal prism+G6 81812 Hexagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal prism+G8 102416 Octagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal prism+G10 123020 Decagonal bipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square pyramid&G4 585 Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal pyramid&G5 6106 Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal pyramid&G6 7127 Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal pyramid&G8 9169 Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal pyramid&G10 112011 Self-dual
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square antiprismG4$H4 10168 Tetragonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal antiprismG5$H5 122010 Pentagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal antiprismG6$H6 162814 Hexagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal antiprismG8$H8 203618 Octagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal antiprismG10$H10 244422 Decagonal trapezohedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Trigonal expanded antitrapezohedronUnknown 122414
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Triangular orthobicupolaUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Tetragonal expanded antitrapezohedronUnknown 163218
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Square orthobicupolaUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal expanded antitrapezohedronUnknown 204022
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal orthobicupolaUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cubic snubKo0 386024 Pentagonal icositetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Dodecahedral snubKi0 9215060 Pentagonal hexecontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cuboctahedral rectateKo5 264824 Deltoidal icositetrahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosidodecahedral rectateKi5 6212060 Deltoidal hexecontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cuboctahedral truncateKo7 267248 Disdyakis dodecahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosidodecahedral truncateKi7 62180120 Disdyakis triacontahedron
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endotrikis antiprismUnknown 10157 Trigonal trapezosemipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endotetrakis antiprismUnknown 13209 Tetragonal trapezosemipyramid
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endopentakis antiprismUnknown 162511 Pentagonal trapezosemipyramid