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24-cell
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In four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}. It is also called C24, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells.
A 4-dimensional ring of 6 face-bonded octahedra, bounded by two intersecting sets of three Clifford parallel great hexagons of different colors, cut a
A 4-dimensional ring of 6 face-bonded octahedra, bounded by two intersecting sets of three Clifford parallel great hexagons of different colors, cut and laid out flat in 3 dimensional space.
Octacube steel sculpture at Pennsylvania State University
Octacube steel sculpture at Pennsylvania State University
Platonic solid
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In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent regular polygons, and the same number of faces meet at each vertex. There are only five such polyhedra:
Kepler's Platonic solid model of the Solar System from Mysterium Cosmographicum (1596)
Kepler's Platonic solid model of the Solar System from Mysterium Cosmographicum (1596)
Icosahedron as a part of Spinoza monument in Amsterdam
Icosahedron as a part of Spinoza monument in Amsterdam
A set of polyhedral dice.
A set of polyhedral dice.
Image: Kepler Hexahedron Earth
Image: Kepler Hexahedron Earth