Icosahedral 120-cell

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Icosahedral 120-cell
Ortho solid 007-uniform polychoron 35p-t0.png
Orthogonal projection
Type Schläfli-Hess polytope
Cells 120 {3,5}
Faces 1200 {3}
Edges 720
Vertices 120
Vertex figure {5,5/2}
Schläfli symbol {3,5,5/2}
Symmetry group H4, [3,3,5]
Coxeter-Dynkin diagram CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png
Dual Small stellated 120-cell
Properties Regular

In geometry, the icosahedral 120-cell, polyicosahedron, faceted 600-cell or icosaplex is a regular star 4-polytope with Schläfli symbol {3,5,5/2}. It is one of 10 regular Schläfli-Hess polytope.

It is constructed by 5 icosahedra around each edge in a pentagrammic figure. The vertex figure is a great dodecahedron.

Related polytopes[edit]

It has the same edge arrangement as the 600-cell, grand 120-cell and great 120-cell, and shares its vertices with all other Schläfli–Hess 4-polytope except the great grand stellated 120-cell (another stellation of the 120-cell).

Orthographic projections by Coxeter planes
H4 - F4
600-cell graph H4.svg
[30]
600-cell t0 p20.svg
[20]
600-cell t0 F4.svg
[12]
H3 A2 / B3 / D4 A3 / B2
600-cell t0 H3.svg
[10]
600-cell t0 A2.svg
[6]
600-cell t0.svg
[4]

As a faceted 600-cell, replacing the simplicial cells of the 600-cell with icosahedral pentagonal polytope cells, it could be seen as a four-dimensional analogue of the great dodecahedron, which replaces the triangular faces of the icosahedron with pentagonal faces. Indeed, the icosahedral 120-cell is dual to the small stellated 120-cell, which could be taken as a 4D analogue of the small stellated dodecahedron, dual of the great dodecahedron.

See also[edit]

References[edit]

External links[edit]