The great icosahedron is one of the four Kepler-Poinsot polyhedra, the nonconvex regular polyhedra, composed of twenty intersecting triangular faces with five triangles meeting at each vertex in a pentagrammic sequence. It can be constructed analogously to the pentagram, its two dimensional analogue, by extending the equilateral triangle faces of the ordinary icosahedron outward until the figure regains regular faces, and the four dimensional grand 600-cell can be seen as its four dimensional analogue built by the same process.
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Source Wikipedia: Kepler-Poinsot polyhedron
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1. Wikipedia: Great icosahedron
Introduction (lede paragraph)Quote, Introduction (lede paragraph)
In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra)
2. Wikipedia: Kepler-Poinsot polyhedron
History section
In 1809, Louis Poinsot rediscovered Kepler's figures by assembling star pentagons around each vertex. He also assembled convex polygons around star vertices to discover two more regular stars, the great icosahedron and great dodecahedron.
- In Branch: Geometry, Lead sentence
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