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The 120-cell.
You probably think dodecahedra are tight. Have you considered trying hyperdodecahedra?
Great thanks to Professor Mark Crawford, who showed me this gem. It may take a little bit to shatter your consciousness, so please be patient. :)
Dodecaplex. Polydodecahedron. Hecatonicosachoron. Dodecacontachoron. Hecatonicosahedroid.
Mathematics is beautiful. <3
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Another View of the Hyperdodecahedron This regular polytope (four-dimensional version of a polyhedron) is rotating in hyperspace. If you could see it there, you'd notice that all 120 dodecahedral cells have the same volume. Created with Stella 4d (site to try it:
Hyperdodecahedron
"a four dimensional polytope composed of 120 dodecahedra and also known as the hyperdodecahedron or hecatonicosachoron"
