icositetrachoron

icosi- (“twenty”) +‎ tetra- (“four”) +‎ -choron (“room”), from Ancient Greek εἴκοσι (eíkosi, “twenty”) τέτταρες (téttares, “four”) and χώρος (khṓros, “room”).

• IPA^(key): /aɪkoʊsɪtɛtɹəˈkoʊɹɔn/

icositetrachoron (plural icositetrachorons or icositetrachora)

1. (mathematics) A four-dimensional object with no regular three-dimensional analogue, constructed out of twenty-four octahedra.
   • 2011, Jin Akiyama, Ikuro Sato, The element number of the convex regular polytopes‎, page 270:

     There are six convex regular 4-polytopes; five of these are the higher dimensional analogs of the Platonic solids, and one additional figure, the icositetrachoron, has no three-dimensional equivalent.

   • 2012, Andrzej Katunin, Fractals based on regular convex polytopes‎, page 56:

     The icositetrachoron (hyperdiamond, octaplex or 24-cell) is the most unique polychoron, because it has no direct analog in any other dimension.

   • 2012, Raymond Aschheim, Spin foam with topologically encoded tetrad on trivalent spin networks‎:

     Shape of Nature comes from a unique, optimally symmetric geometric object: the sixth platonic element, the icositetrachoron (or 24-cell regular polytope), crystallized as a hyperdiamond network, mathematically and physically made of loops and connections.

• 24-cell