| bgcolor=#e7dcc3 colspan=2 | Small triambic icosahedron | |
|---|---|---|
| align=center colspan=2 | ||
| Type | Dual uniform polyhedron | |
| Index | DU30, 2/59, W26 | |
| Elements (As a star polyhedron) | F = 20, E = 60 V = 32 (χ = -8) | |
| Symmetry group | icosahedral (Ih) | |
| Dual polyhedron | small ditrigonal icosidodecahedron | |
The faces are equilateral hexagons, with alternating angles of
| \arccos(- | 1 |
| 4 |
) ≈ 104.47751218593\circ
| \arccos( | 1 |
| 4 |
)+60\circ ≈ 135.52248781407\circ
| \arccos(- | 1 |
| 3 |
) ≈ 109.47122063449
The external surface of the small triambic icosahedron (removing the parts of each hexagonal face that are surrounded by other faces, but interpreting the resulting disconnected plane figures as still being faces) coincides with one of the stellations of the icosahedron.[2] If instead, after removing the surrounded parts of each face, each resulting triple of coplanar triangles is considered to be three separate faces, then the result is one form of the triakis icosahedron, formed by adding a triangular pyramid to each face of an icosahedron.
The dual polyhedron of the small triambic icosahedron is the small ditrigonal icosidodecahedron. As this is a uniform polyhedron, the small triambic icosahedron is a uniform dual. Other uniform duals whose exterior surfaces are stellations of the icosahedron are the medial triambic icosahedron and the great triambic icosahedron.
. Magnus Wenninger . Polyhedron Models . Cambridge University Press . 1974 . 0-521-09859-9 . (p. 46, Model W26, triakis icosahedron)
. Magnus Wenninger . Dual Models . Cambridge University Press . 1983 . 0-521-54325-8 . (pp. 42 - 46, dual to uniform polyhedron W70)
. Branko Grünbaum . Can every face of a polyhedron have many sides? . 1773/4593 . 2512345 . 9–26 . Comap, Inc. . Bedford, Massachusetts . Geometry, games, graphs and education: the Joe Malkevitch Festschrift . 2008.