Polydodecahedron

The dodecahedron is a solid having 12 pentagonal faces.

This sculpture, by Marc Pelletier, is a three-dimensional shadow, or "projection", of the analogous four-dimensional figure called the "polydodecahedron", or "120-cell", whose 120 cells (or three-dimensional
faces) are regular dodecahedra.

The sculpture is a copy of one that was presented by an anonymous donor to the Fields Mathematical Institute in Toronto to honor the 95th birthday of the famous geometer H.S.M.Coxeter in February 2002. The same donor presented this one to the Princeton University Mathematics Department in honor of Professor John H. Conway.

Compare the sculpture to the three shadows of an ordinary dodecahedron shown below.

Count the 12 Pentagons in these projections of a dodecahedron:     Face-first   Edge-first   Vertex-first 1+5 + 5+1   2+2 +4+ 2+2   3+3 + 3+3 Front   Back   Front Walls Back   Front   Back     The walls are projected into lines     Now count the 120 dodecahedra in the sculpture: 1+12+20+12 + 30 + 12+20+12+1 Front Walls Back   These walls are projected edge-first into planes

The Platonic solid called the "regular dodecahedron" has 12 faces that are regular pentagons. If you don't know what a dodecahedron looks like, you can see one at the center of the sculpture.

Although the polydodecahedron is a gemlike object living in a space that is inaccessible to us, we can gain some appreciation of its beauty from Marc's sculpture.

The dodecahedron at the center of the sculpture is surrounded at its faces by 12 others that have been only slightly foreshortened by the projection.

Proceeding outwards, we find beyond its vertices 20 others that are slightly more so, then a further 12 that have been considerably flattened by the foreshortening. Finally, the figure is bounded by 30 "walls" formed by dodecahedra that are seen "edge-on" and so are totally flat.