List of polyhedra by facet layout (Meta, 12)

From Hi.gher. Space

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 +
<[#ontology [kind meta] [cats 3D Polytope Facet_Layout_Diagram]]>
{|class='shapelist' style='width:100%;'
{|class='shapelist' style='width:100%;'
!colspan='3'|Parent
!colspan='3'|Parent
Line 10: Line 11:
!style='width:8%;' class='key'|Edges
!style='width:8%;' class='key'|Edges
!style='width:8%;' class='key'|Vertices
!style='width:8%;' class='key'|Vertices
-
!style='width:10%;'|[[Facet layout]]
+
!style='width:10%;'|Facet layout
!style='width:20%;'|Name
!style='width:20%;'|Name
!style='width:8%;'|SSC2
!style='width:8%;'|SSC2
Line 36: Line 37:
|- class='row2'
|- class='row2'
|{{FLD|a3|i|a4|cr}}
|{{FLD|a3|i|a4|cr}}
-
|[[Cuboctahedron]]||Ko2
+
|[[Stauromesohedron]]||Ko2
|14||24||12
|14||24||12
-
|[[Rhombic dodecahedron]]
+
|''Unknown''
 +
|[[Rhombic dodecahedron]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a3|i|a5|cr}}
|{{FLD|a3|i|a5|cr}}
-
|[[Icosidodecahedron]]||Ki2
+
|[[Rhodomesohedron]]||Ki2
|32||60||30
|32||60||30
-
|[[Rhombic triacontahedron]]
+
|''Unknown''
 +
|[[Rhombic triacontahedron]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
Line 50: Line 53:
|[[Tetrahedral truncate]]||Kt3
|[[Tetrahedral truncate]]||Kt3
|8||18||12
|8||18||12
-
|[[Triakis tetrahedron]]
+
|''Unknown''
 +
|[[Triakis tetrahedron]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a3|i|a4|er}}
|{{FLD|a3|i|a4|er}}
|[[Cubic truncate]]||Ko3
|[[Cubic truncate]]||Ko3
|14||36||24
|14||36||24
-
|[[Triakis octahedron]]
+
|''Unknown''
 +
|[[Triakis octahedron]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a3|i|a5|er}}
|{{FLD|a3|i|a5|er}}
|[[Dodecahedral truncate]]||Ki3
|[[Dodecahedral truncate]]||Ki3
|32||90||60
|32||90||60
-
|[[Triakis icosahedron]]
+
|''Unknown''
 +
|[[Triakis icosahedron]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a4|i|a3|er}}
|{{FLD|a4|i|a3|er}}
|[[Octahedral truncate]]||Ko6
|[[Octahedral truncate]]||Ko6
|14||36||24
|14||36||24
-
|[[Tetrakis hexahedron]]
+
|''Unknown''
 +
|[[Tetrakis hexahedron]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a5|i|a3|er}}
|{{FLD|a5|i|a3|er}}
|[[Icosahedral truncate]]||Ki6
|[[Icosahedral truncate]]||Ki6
|32||90||60
|32||90||60
-
|[[Pentakis dodecahedron]]
+
|''Unknown''
 +
|[[Pentakis dodecahedron]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
Line 77: Line 85:
|[[Triangular prism]]||+G3
|[[Triangular prism]]||+G3
|5||9||6
|5||9||6
-
|[[Triangular bipyramid]]
+
|''Unknown''
 +
|[[Triangular bipyramid]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a5|i|a2|er}}
|{{FLD|a5|i|a2|er}}
|[[Pentagonal prism]]||+G5
|[[Pentagonal prism]]||+G5
|7||15||10
|7||15||10
-
|[[Pentagonal bipyramid]]
+
|''Unknown''
 +
|[[Pentagonal bipyramid]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a6|i|a2|er}}
|{{FLD|a6|i|a2|er}}
|[[Hexagonal prism]]||+G6
|[[Hexagonal prism]]||+G6
|8||18||12
|8||18||12
-
|[[Hexagonal bipyramid]]
+
|''Unknown''
 +
|[[Hexagonal bipyramid]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a8|i|a2|er}}
|{{FLD|a8|i|a2|er}}
|[[Octagonal prism]]||+G8
|[[Octagonal prism]]||+G8
|10||24||16
|10||24||16
-
|[[Octagonal bipyramid]]
+
|''Unknown''
 +
|[[Octagonal bipyramid]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a10|i|a2|er}}
|{{FLD|a10|i|a2|er}}
|[[Decagonal prism]]||+G10
|[[Decagonal prism]]||+G10
|12||30||20
|12||30||20
-
|[[Decagonal bipyramid]]
+
|''Unknown''
 +
|[[Decagonal bipyramid]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
Line 104: Line 117:
|[[Square pyramid]]||&G4
|[[Square pyramid]]||&G4
|5||8||5
|5||8||5
-
|Self-dual
+
|colspan='3'|''Self-dual''
|- class='row1'
|- class='row1'
|{{FLD|a5|i|ade|cr|e5}}
|{{FLD|a5|i|ade|cr|e5}}
|[[Pentagonal pyramid]]||&G5
|[[Pentagonal pyramid]]||&G5
|6||10||6
|6||10||6
-
|Self-dual
+
|colspan='3'|''Self-dual''
|- class='row2'
|- class='row2'
|{{FLD|a6|i|ade|cr|e6}}
|{{FLD|a6|i|ade|cr|e6}}
|[[Hexagonal pyramid]]||&G6
|[[Hexagonal pyramid]]||&G6
|7||12||7
|7||12||7
-
|Self-dual
+
|colspan='3'|''Self-dual''
|- class='row1'
|- class='row1'
|{{FLD|a8|i|ade|cr|e8}}
|{{FLD|a8|i|ade|cr|e8}}
|[[Octagonal pyramid]]||&G8
|[[Octagonal pyramid]]||&G8
|9||16||9
|9||16||9
-
|Self-dual
+
|colspan='3'|''Self-dual''
|- class='row2'
|- class='row2'
|{{FLD|a10|i|ade|cr|e10}}
|{{FLD|a10|i|ade|cr|e10}}
|[[Decagonal pyramid]]||&G10
|[[Decagonal pyramid]]||&G10
|11||20||11
|11||20||11
-
|Self-dual
+
|colspan='3'|''Self-dual''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
Line 131: Line 144:
|[[Square antiprism]]||G4$H4
|[[Square antiprism]]||G4$H4
|10||16||8
|10||16||8
-
|[[Tetragonal trapezohedron]]
+
|''Unknown''
 +
|[[Tetragonal trapezohedron]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a5|i|ade|cr|e10}}
|{{FLD|a5|i|ade|cr|e10}}
|[[Pentagonal antiprism]]||G5$H5
|[[Pentagonal antiprism]]||G5$H5
|12||20||10
|12||20||10
-
|[[Pentagonal trapezohedron]]
+
|''Unknown''
 +
|[[Pentagonal trapezohedron]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a6|i|ade|cr|e12}}
|{{FLD|a6|i|ade|cr|e12}}
|[[Hexagonal antiprism]]||G6$H6
|[[Hexagonal antiprism]]||G6$H6
|16||28||14
|16||28||14
-
|[[Hexagonal trapezohedron]]
+
|''Unknown''
 +
|[[Hexagonal trapezohedron]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a8|i|ade|cr|e16}}
|{{FLD|a8|i|ade|cr|e16}}
|[[Octagonal antiprism]]||G8$H8
|[[Octagonal antiprism]]||G8$H8
|20||36||18
|20||36||18
-
|[[Octagonal trapezohedron]]
+
|''Unknown''
 +
|[[Octagonal trapezohedron]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a10|i|ade|cr|e20}}
|{{FLD|a10|i|ade|cr|e20}}
|[[Decagonal antiprism]]||G10$H10
|[[Decagonal antiprism]]||G10$H10
|24||44||22
|24||44||22
-
|[[Decagonal trapezohedron]]
+
|''Unknown''
 +
|[[Decagonal trapezohedron]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
|- class='row2'
|- class='row2'
|{{FLD|left=e3|dsel|aq|dsrmel|adl|er}}
|{{FLD|left=e3|dsel|aq|dsrmel|adl|er}}
-
|[[Trigonal expanded antitrapezohedron]]||Unknown
+
|[[Trigonal expanded antitrapezohedron]]||''Unknown''
|12||24||14
|12||24||14
|{{FLD|a3|i|adr|edm|adl|er}}
|{{FLD|a3|i|adr|edm|adl|er}}
-
|[[Triangular orthobicupola]]||Unknown
+
|[[Triangular orthobicupola]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|left=e4|dsel|aq|dsrmel|adl|er}}
|{{FLD|left=e4|dsel|aq|dsrmel|adl|er}}
-
|[[Tetragonal expanded antitrapezohedron]]||Unknown
+
|[[Tetragonal expanded antitrapezohedron]]||''Unknown''
|16||32||18
|16||32||18
|{{FLD|a4|i|adr|edm|adl|er}}
|{{FLD|a4|i|adr|edm|adl|er}}
-
|[[Square orthobicupola]]||Unknown
+
|[[Square orthobicupola]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|left=e5|dsel|aq|dsrmel|adl|er}}
|{{FLD|left=e5|dsel|aq|dsrmel|adl|er}}
-
|[[Pentagonal expanded antitrapezohedron]]||Unknown
+
|[[Pentagonal expanded antitrapezohedron]]||''Unknown''
|20||40||22
|20||40||22
|{{FLD|a5|i|adr|edm|adl|er}}
|{{FLD|a5|i|adr|edm|adl|er}}
-
|[[Pentagonal orthobicupola]]||Unknown
+
|[[Pentagonal orthobicupola]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
|- class='row1'
|- class='row1'
|{{FLD|a3|i|ate|i|a4|cr}}
|{{FLD|a3|i|ate|i|a4|cr}}
-
|[[Cubic snub]]||Ko0
+
|[[Snub staurohedron]]||Ko0
|38||60||24
|38||60||24
-
|[[Pentagonal icositetrahedron]]
+
|''Unknown''
 +
|[[Pentagonal icositetrahedron]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a3|i|ate|i|a5|cr}}
|{{FLD|a3|i|ate|i|a5|cr}}
-
|[[Dodecahedral snub]]||Ki0
+
|[[Snub rhodohedron]]||Ki0
|92||150||60
|92||150||60
-
|[[Pentagonal hexecontahedron]]
+
|''Unknown''
 +
|[[Pentagonal hexecontahedron]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
|- class='row1'
|- class='row1'
|{{FLD|a3|i|a2|i|a4|cr}}
|{{FLD|a3|i|a2|i|a4|cr}}
-
|[[Cuboctahedral rectate]]||Ko5
+
|[[Stauroperihedron]]||Ko5
|26||48||24
|26||48||24
-
|[[Deltoidal icositetrahedron]]
+
|''Unknown''
 +
|[[Deltoidal icositetrahedron]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a3|i|a2|i|a5|cr}}
|{{FLD|a3|i|a2|i|a5|cr}}
-
|[[Icosidodecahedral rectate]]||Ki5
+
|[[Rhodoperihedron]]||Ki5
|62||120||60
|62||120||60
-
|[[Deltoidal hexecontahedron]]
+
|''Unknown''
 +
|[[Deltoidal hexecontahedron]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
|- class='row1'
|- class='row1'
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}}
|{{FLD|a2tr|ti|a3tm|ti|a4tl|cr}}
-
|[[Cuboctahedral truncate]]||Ko7
+
|[[Stauropantohedron]]||Ko7
|26||72||48
|26||72||48
-
|[[Disdyakis dodecahedron]]
+
|''Unknown''
 +
|[[Disdyakis dodecahedron]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}}
|{{FLD|a2tr|ti|a3tm|ti|a5tl|cr}}
-
|[[Icosidodecahedral truncate]]||Ki7
+
|[[Rhodopantohedron]]||Ki7
|62||180||120
|62||180||120
-
|[[Disdyakis triacontahedron]]
+
|''Unknown''
 +
|[[Disdyakis triacontahedron]]||''Unknown''
|-
|-
|class='cat' colspan='9'|
|class='cat' colspan='9'|
|- class='row1'
|- class='row1'
|{{FLD|a3|i|adr|dm|adl|i|asr|dser}}
|{{FLD|a3|i|adr|dm|adl|i|asr|dser}}
-
|[[Endotrikis antiprism]]||Unknown
+
|[[Endotrikis antiprism]]||''Unknown''
|10||15||7
|10||15||7
-
|[[Trigonal trapezosemipyramid]]
+
|''Unknown''
 +
|[[Trigonal trapezosemipyramid]]||''Unknown''
|- class='row2'
|- class='row2'
|{{FLD|a4|i|adr|dm|adl|i|asr|dser}}
|{{FLD|a4|i|adr|dm|adl|i|asr|dser}}
-
|[[Endotetrakis antiprism]]||Unknown
+
|[[Endotetrakis antiprism]]||''Unknown''
|13||20||9
|13||20||9
-
|[[Tetragonal trapezosemipyramid]]
+
|''Unknown''
 +
|[[Tetragonal trapezosemipyramid]]||''Unknown''
|- class='row1'
|- class='row1'
|{{FLD|a5|i|adr|dm|adl|i|asr|dser}}
|{{FLD|a5|i|adr|dm|adl|i|asr|dser}}
-
|[[Endopentakis antiprism]]||Unknown
+
|[[Endopentakis antiprism]]||''Unknown''
|16||25||11
|16||25||11
-
|[[Pentagonal trapezosemipyramid]]
+
|''Unknown''
 +
|[[Pentagonal trapezosemipyramid]]||''Unknown''
 +
|-
 +
|class='cat' colspan='9'|
 +
|- class='row1'
 +
|{{FLD|a3|i|adesr|di|asl|i|a3|cr}}
 +
|[[Tridiminished icosahedron]]||''Unknown''
 +
|8||15||9
 +
|''Unknown''
 +
|''Unknown''||''Unknown''
 +
|- class='row2'
 +
|{{FLD|a2tr|ti|asrtm|ditm|aqtm|editm|atlsl|cr}}
 +
|[[Bilunabirotunda]]||''Unknown''
 +
|14||26||14
 +
|''Unknown''
 +
|''Unknown''||''Unknown''
|}
|}
[[Category:Trishapes|$]]
[[Category:Trishapes|$]]

Latest revision as of 22:47, 12 March 2014

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)
StauromesohedronKo2 142412 Unknown Rhombic dodecahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
RhodomesohedronKi2 326030 Unknown Rhombic triacontahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Tetrahedral truncateKt3 81812 Unknown Triakis tetrahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Cubic truncateKo3 143624 Unknown Triakis octahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Dodecahedral truncateKi3 329060 Unknown Triakis icosahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octahedral truncateKo6 143624 Unknown Tetrakis hexahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Icosahedral truncateKi6 329060 Unknown Pentakis dodecahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Triangular prism+G3 596 Unknown Triangular bipyramidUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal prism+G5 71510 Unknown Pentagonal bipyramidUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal prism+G6 81812 Unknown Hexagonal bipyramidUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal prism+G8 102416 Unknown Octagonal bipyramidUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal prism+G10 123020 Unknown Decagonal bipyramidUnknown
(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$H4 10168 Unknown Tetragonal trapezohedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Pentagonal antiprismG5$H5 122010 Unknown Pentagonal trapezohedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Hexagonal antiprismG6$H6 162814 Unknown Hexagonal trapezohedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Octagonal antiprismG8$H8 203618 Unknown Octagonal trapezohedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Decagonal antiprismG10$H10 244422 Unknown Decagonal trapezohedronUnknown
(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)
Snub staurohedronKo0 386024 Unknown Pentagonal icositetrahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Snub rhodohedronKi0 9215060 Unknown Pentagonal hexecontahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
StauroperihedronKo5 264824 Unknown Deltoidal icositetrahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
RhodoperihedronKi5 6212060 Unknown Deltoidal hexecontahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
StauropantohedronKo7 267248 Unknown Disdyakis dodecahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
RhodopantohedronKi7 62180120 Unknown Disdyakis triacontahedronUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endotrikis antiprismUnknown 10157 Unknown Trigonal trapezosemipyramidUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endotetrakis antiprismUnknown 13209 Unknown Tetragonal trapezosemipyramidUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Endopentakis antiprismUnknown 162511 Unknown Pentagonal trapezosemipyramidUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
Tridiminished icosahedronUnknown 8159 Unknown UnknownUnknown
(image) (image) (image) (image) (image) (image) (image) (image) (image) (image)
BilunabirotundaUnknown 142614 Unknown UnknownUnknown
Retrieved from "http://hi.gher.space/wiki/List_of_polyhedra_by_facet_layout"