In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram.
It is also called the echidnahedron. This polyhedron is the seventeenth stellation of the icosahedron, and given as Wenninger model index 42.
As a geometrical figure, it has two interpretations, described below:
- As an irregular star (self-intersecting) polyhedron with 20 identical self-intersecting enneagrammic faces, 90 edges, 60 vertices.
- As a simple polyhedron with 180 triangular faces (60 isosceles, 120 scalene), 270 edges, and 92 vertices. This interpretation is useful for polyhedron model building.
Johannes Kepler researched stellations that create regular star polyhedra (the Kepler-Poinsot polyhedra) in 1619, but the complete icosahedron, with irregular faces, was first studied in 1900 by Max Brückner.
Read more about Final Stellation Of The Icosahedron: History
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