Small stellated 120-cell

Small stellated 120-cell

Orthogonal projection
TypeSchläfli-Hess polytope
Cells120 {5/2,5}
Faces720 {5/2}
Vertex figure{5,3}
Schläfli symbol {5/2,5,3}
Coxeter-Dynkin diagram
Symmetry groupH4, [3,3,5]
Dual Icosahedral 120-cell
Properties Regular

In geometry, the small stellated 120-cell or stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,3}. It is one of 10 regular Schläfli-Hess polytopes.

Related polytopes

It has the same edge arrangement as the great grand 120-cell, and also shares its 120 vertices with the 600-cell and eight other regular star 4-polytope. It may also be seen as the first stellation of the 120-cell. In this sense it could be seen as analogous to the three-dimensional small stellated dodecahedron, which is the first stellation of the dodecahedron. Indeed, the small stellated 120-cell is dual to the icosahedral 120-cell, which could be taken as a 4D analogue of the great dodecahedron, dual of the small stellated dodecahedron.

The edges of the small stellated 120-cell are τ2 as long as those of the 120-cell core inside the 4-polytope.

Orthographic projections by Coxeter planes
H3 A2 / B3 / D4 A3 / B2

See also


External links

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