Icosahedral 120-cell

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.

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).

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.

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