Stella Octangula -- from Wolfram MathWorld

Stellated octahedron - Wikipedia

Generation of an icosahedron by the intersection of five tetrahedra: geometrical and crystallographic features of the intermediate polyhedra

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Stella Octangula -- from Wolfram MathWorld

Another construction for the stella octangula numbers. Authors

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Altered stella octangula - Polytope Wiki

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Geometric Model by A. Harry Wheeler, Stella Octangula or Stellated Octahedron or Compount of Two Tetrahedra