16-cell
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In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid [sic?].
A 4-dimensional ring of 8 face-bonded tetrahedra, seen in the Boerdijk–Coxeter helix, bounded by three eight-edge circular paths of different colors, cut and laid out flat in 3-dimensional space. It contains an isocline axis (not shown), a helical circle of circumference 4𝝅 that twists through all four dimensions and visits all 8 vertices. The two blue-blue-yellow triangles at either end of the cut ring are the same object.
Octahedron
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In geometry, an octahedron is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
Fluorite octahedron.
Two identically formed Rubik's Snakes can approximate an octahedron.
Image: Octahedron