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


  • IPA(key): /aɪkoʊsɨtɛtɹəˈkoʊɹɔn/


icositetrachoron (plural icositetrachorons or icositetrachora)

  1. (mathematics) A four-dimensional object equivalent to a hexagon, constructed out of twenty-four octahedra.
    • 2011, Jin Akiyama and Ikuro Sato, The element number of the convex regular polytopes[1], 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[2], 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[3]:
      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.