Uniform Polyhedra --- List

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)

Virtual Polyhedra, (c) 1996,George W. Hart