The uniform polyhedra are listed here
in groups of three: a solid, its dual, and their compound. An image of
the dual face is also available for each. The notation in parentheses is
a Wythoff symbol which characterizes the derivation of each. They are listed
here by symmetry goup.
Prism symmetry (up to order 10)
- triangular prism (2 3 | 2)
- triangular dipyramid (face)
- compound of
triangular prism and dual
- square antiprism (| 2 2 4)
- square trapezohedron (face)
- compound of
square antiprism and dual
- pentagonal prism (2 5 | 2)
- pentagonal dipyramid (face)
- compound of
pentagonal prism and dual
- pentagonal antiprism (|
2 2 5)
- pentagonal trapezohedron
(face)
- compound
of pentagonal antiprism and dual
- pentagrammatic prism (2
5/2 | 2)
- pentagrammatic dipyramid
(face)
- compound
of pentagrammatic prism and dual
- pentagrammatic antiprism
(| 2 2 5/2)
- pentagrammatic trapezohedron
(face)
- compound
of pentagrammatic antiprism and dual
- pentagrammatic
crossed antiprism (| 2 2 5/3)
- pentagrammatic
concave trapezohedron (face)
- compound
of pentagrammatic crossed antiprism and dual
- hexagonal prism (2 6 | 2)
- hexagonal dipyramid (face)
- compound of
hexagonal prism and dual
- hexagonal antiprism (| 2
2 6)
- hexagonal trapezohedron
(face)
- compound
of hexagonal antiprism and dual
- heptagonal prism (2 7 | 2)
- heptagonal dipyramid (face)
- compound of
heptagonal prism and dual
- heptagonal antiprism (|
2 2 7)
- heptagonal trapezohedron
(face)
- compound
of heptagonal antiprism and dual
- octagonal prism (2 8 | 2)
- octagonal dipyramid (face)
- compound of
octagonal prism and dual
- octagonal antiprism (| 2
2 8)
- octagonal trapezohedron
(face)
- compound
of octagonal antiprism and dual
- enneagonal prism (2 9 | 2)
- enneagonal dipyramid (face)
- compound of
enneagonal prism and dual
- enneagonal antiprism (|
2 2 9)
- enneagonal trapezohedron
(face)
- compound
of enneagonal antiprism and dual
- decagonal prism (2 10 | 2)
- decagonal dipyramid (face)
- compound of
decagonal prism and dual
- decagonal antiprism (| 2
2 10)
- decagonal trapezohedron
(face)
- compound
of decagonal antiprism and dual
Tetrahedral Symmetry
- tetrahedron (3 | 2 3)
- tetrahedron (face)
- compound of tetrahedron
and dual
- truncated tetrahedron
(2 3 | 3)
- triakistetrahedron (face)
- compound
of truncated tetrahedron and dual
- tetrahemihexahedron (3/2
3 | 2)
- tetrahemihexacron
- compound
of tetrahemihexahedron and dual
Octahedral Symmetry
- octahemioctahedron (3/2 3
| 3)
- octahemioctacron
- compound
of octahemioctahedron and dual
- octahedron (4 | 2 3)
- cube (face)
- compound of octahedron
and dual
- cube (3 | 2 4)
- octahedron (face)
- compound of cube and dual
- cuboctahedron (2 | 3 4)
- rhombic dodecahedron (face)
- compound of cuboctahedron
and dual
- truncated octahedron (2
4 | 3)
- tetrakishexahedron (face)
- compound
of truncated octahedron and dual
- truncated cube (2 3 | 4)
- triakisoctahedron (face)
- compound of
truncated cube and dual
- rhombicuboctahedron (3 4
| 2)
- trapezoidal icositetrahedron
(face)
- compound
of rhombicuboctahedron and dual
- truncated cuboctahedron
(2 3 4 |)
- disdyakisdodecahedron
(face)
- compound
of truncated cuboctahedron and dual
- snub cuboctahedron (| 2 3
4)
- pentagonal icositetrahedron
(face)
- compound
of snub cuboctahedron and dual
- small cubicuboctahedron
(3/2 4 | 4)
- small hexacronic
icositetrahedron (face)
- compound
of small cubicuboctahedron and dual
- great cubicuboctahedron
(3 4 | 4/3)
- great hexacronic
icositetrahedron (face)
- compound
of great cubicuboctahedron and dual
- cubohemioctahedron (4/3 4
| 3)
- hexahemioctacron
- compound
of cubohemioctahedron and dual
- cubitruncated cuboctahedron
(4/3 3 4 |)
- tetradyakishexahedron
(face)
- compound
of cubitruncated cuboctahedron and dual
- great rhombicuboctahedron
(3/2 4 | 2)
- great trapezoidal
icositetrahedron (face)
- compound
of great rhombicuboctahedron and dual
- small rhombicube (3/2 2 4 |)
- small rhombihexacron (face)
- compound of
small rhombicube and dual
- stellated truncated cube
(2 3 | 4/3)
- great triakisoctahedron
(face)
- compound
of stellated truncated cube and dual
- great truncated cuboctahedron
(4/3 2 3 |)
- great disdyakisdodecahedron
(face)
- compound
of great truncated cuboctahedron and dual
- great rhombicube (4/3 3/2 2
|)
- great rhombihexacron (face)
- compound of
great rhombicube and dual
Icosahedral Symmetry
- icosahedron (5 | 2 3)
- dodecahedron (face)
- compound of icosahedron
and dual
- dodecahedron (3 | 2 5)
- icosahedron (face)
- compound of dodecahedron
and dual
- icosidodecahedron (2 | 3 5)
- rhombic triacontahedron
(face)
- compound
of icosidodecahedron and dual
- truncated icosahedron
(2 5 | 3)
- pentakisdodecahedron (face)
- compound
of truncated icosahedron and dual
- truncated dodecahedron
(2 3 | 5)
- triakisicosahedron (face)
- compound
of truncated dodecahedron and dual
- rhombicosidodecahedron
(3 5 | 2)
- trapezoidal hexecontahedron
(face)
- compound
of rhombicosidodecahedron and dual
- truncated icosidodecahedron
(2 3 5 |)
- disdyakistriacontahedron
(face)
- compound
of truncated icosidodecahedron and dual
- snub icosidodecahedron
(| 2 3 5)
- pentagonal hexecontahedron
(face)
- compound
of snub icosidodecahedron and dual
- small triambic
icosidodecahedron (3 | 5/2 3)
- small triambic icosahedron
(face)
- compound
of small triambic icosidodecahedron and dual
- small icosic icosidodecahedron
(5/2 3 | 3)
- small icosacronic
hexecontahedron (face)
- compound
of small icosic icosidodecahedron and dual
- snub disicosidodecahedron
(| 5/2 3 3)
- hexagonal hexecontahedron
(face)
- compound
of snub disicosidodecahedron and dual
- small dodecicosidodecahedron
(3/2 5 | 5)
- small dodecacronic
hexecontahedron (face)
- compound
of small dodecicosidodecahedron and dual
- small stellated dodecahedron
(5 | 2 5/2)
- great dodecahedron (face)
- compound
of small stellated dodecahedron and dual
- great dodecahedron (5/2 |
2 5)
- small stellated dodecahedron
(face)
- compound
of great dodecahedron and dual
- dodecadodecahedron (2 | 5/2
5)
- medial rhombic triacontahedron
(face)
- compound
of dodecadodecahedron and dual
- great truncated dodecahedron
(2 5/2 | 5)
- small stellapentakisdodecahedron
(face)
- compound
of great truncated dodecahedron and dual
- rhombidodecadodecahedron
(5/2 5 | 2)
- medial trapezoidal
hexecontahedron (face)
- compound
of rhombidodecadodecahedron and dual
- small rhombidodecahedron
(2 5/2 5 |)
- small rhombidodecacron
(face)
- compound
of small rhombidodecahedron and dual
- snub dodecadodecahedron
(| 2 5/2 5)
- medial pentagonal
hexecontahedron (face)
- compound
of snub dodecadodecahedron and dual
- triambic dodecadodecahedron
(3 | 5/3 5)
- medial triambic icosahedron
(face)
- compound
of triambic dodecadodecahedron and dual
- great dodekic icosidodecahedron
(3 5 | 5/3)
- great dodecacronic
hexecontahedron (face)
- compound
of great dodekic icosidodecahedron and dual
- small dodekic icosidodecahedron
(5/3 3 | 5)
- small dodecacronic
hexecontahedron (face)
- compound
of small dodekic icosidodecahedron and dual
- icosidodecadodecahedron
(5/3 5 | 3)
- medial icosacronic
hexecontahedron (face)
- compound
of icosidodecadodecahedron and dual
- icositruncated
dodecadodecahedron (5/3 3 5 |)
- tridyakisicosahedron (face)
- compound
of icositruncated dodecadodecahedron and dual
- snub icosidodecadodecahedron
(| 5/3 3 5)
- medial hexagonal
hexecontahedron (face)
- compound
of snub icosidodecadodecahedron and dual
- great triambic
icosidodecahedron (3/2 | 3 5)
- great triambic icosahedron
(face)
- compound
of great triambic icosidodecahedron and dual
- great icosic icosidodecahedron
(3/2 5 | 3)
- great icosacronic
hexecontahedron (face)
- compound
of great icosic icosidodecahedron and dual
- small icosihemidodecahedron
(3/2 3 | 5)
- small icosihemidodecacron
- compound
of small icosihemidodecahedron and dual
- small dodecicosahedron
(3/2 3 5 |)
- small dodecicosacron (face)
- compound
of small dodecicosahedron and dual
- small dodecahemidodecahedron
(5/4 5 | 5)
- small dodecahemidodecacron
- compound
of small dodecahemidodecahedron and dual
- great stellated dodecahedron
(3 | 2 5/2)
- great icosahedron (face)
- compound
of great stellated dodecahedron and dual
- great icosahedron (5/2 | 2
3)
- great stellated dodecahedron
(face)
- compound
of great icosahedron and dual
- great icosidodecahedron
(2 | 5/2 3)
- great rhombic triacontahedron
(face)
- compound
of great icosidodecahedron and dual
- great truncated icosahedron
(2 5/2 | 3)
- great stellapentakisdodecahedron
(face)
- compound
of great truncated icosahedron and dual
- rhombicosahedron (2 5/2 3 |)
- rhombicosacron (face)
- compound of
rhombicosahedron and dual
- great snub icosidodecahedron
(| 2 5/2 3)
- great pentagonal
hexecontahedron (face)
- compound
of great snub icosidodecahedron and dual
- small stellated
truncated dodecahedron (2 5 | 5/3)
- great pentakisdodekahedron
(face)
- compound
of small stellated truncated dodecahedron and dual
- great truncated
dodecadodecahedron (5/3 2 5 |)
- medial disdyakistriacontahedron
(face)
- compound
of great truncated dodecadodecahedron and dual
- vertisnub dodecadodecahedron
(| 5/3 2 5)
- medial
inverted pentagonal hexecontahedron (face)
- compound
of vertisnub dodecadodecahedron and dual
- great dodecicosidodecahedron
(5/2 3 | 5/3)
- great dodecacronic
hexecontahedron (face)
- compound
of great dodecicosidodecahedron and dual
- great dodecahemiicosahedron
(5/3 5/2 | 3)
- great dodecahemiicosacron
- compound
of great dodecahemiicosahedron and dual
- great dodecicosahedron
(5/3 5/2 3 |)
- great dodecicosacron (face)
- compound
of great dodecicosahedron and dual
- great snub icosidisdodecahedron
(| 5/3 5/2 3)
- great hexagonal
hexecontahedron (face)
- compound
of great snub icosidisdodecahedron and dual
- small dodecahemiicosahedron
(5/4 5 | 3)
- small dodecahemiicosacron
- compound
of small dodecahemiicosahedron and dual
- great stellated
truncated dodecahedron (2 3 | 5/3)
- great triakisicosahedron
(face)
- compound
of great stellated truncated dodecahedron and dual
- great rhombicosidodecahedron
(5/3 3 | 2)
- great trapezoidal
hexecontahedron (face)
- compound
of great rhombicosidodecahedron and dual
- great truncated
icosidodecahedron (5/3 2 3 |)
- great disdyakistriacontahedron
(face)
- compound
of great truncated icosidodecahedron and dual
- great vertisnub
icosidodecahedron (| 5/3 2 3)
- great
inverted pentagonal hexecontahedron (face)
- compound
of great vertisnub icosidodecahedron and dual
- great dodecahemidodecahedron
(5/3 5/2 | 5/3)
- great dodecahemidodecacron
- compound
of great dodecahemidodecahedron and dual
- great icosihemidodecahedron
(3/2 3 | 5/3)
- great icosihemidodecacron
- compound
of great icosihemidodecahedron and dual
- retrosnub disicosidodecahedron
(| 3/2 3/2 5/2)
- small hexagrammatic
hexecontahedron (face)
- compound
of retrosnub disicosidodecahedron and dual
- great rhombidodecahedron
(3/2 5/3 2 |)
- great rhombidodecacron
(face)
- compound
of great rhombidodecahedron and dual
- great retrosnub
icosidodecahedron (| 3/2 5/3 2)
- great pentagrammatic
hexecontahedron (face)
- compound
of great retrosnub icosidodecahedron and dual
- great snub disicosidisdodecahedron
(| 3/2 5/3 3 5/2)
