Vertex-first-120-cell-core

3D Model

This is the center of a vertex-first projection of the 120-cell, or hyperdodecahedron, a 4-dimensional polytope. In four dimensions, it is a regular polytope consisting of 120 regular dodecahedra, evenly tiling the 3D “surface” of the hypersphere.

That polytope can be projected down into normal, Euclidean 3-space at different angles. Zometool was originally conceived by Marc Pelletier based on the cell-first projection, which has a regular dodecahedral cell at the center. This model shows the “opposite” projection, with a vertex at the center.

In this projection, there are no regular dodecahedra at all, but the four tetrahedrally-arranged central dodecahedra are all congruent.

You can build this in reality using yellow and green Zometool struts, in combination with maroon, olive, and lavender vZome struts, available from Shapeways as 3D-prints.