Great icosahedron

Great icosahedron
Type Kepler–Poinsot polyhedron
Stellation core icosahedron
Elements F = 20, E = 30
V = 12 (χ = 2)
Faces by sides 20{3}
Schläfli symbol {3,52}
Face configuration V(53)/2
Wythoff symbol 52 | 2 3
Coxeter diagram
Symmetry group Ih, H3, [5,3], (*532)
References U53, C69, W41
Properties Regular nonconvex deltahedron

(35)/2
(Vertex figure)

Great stellated dodecahedron
(dual polyhedron)
3D model of a great icosahedron

In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3,52} and Coxeter-Dynkin diagram of . It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence.

The great icosahedron can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of the (n–1)-dimensional simplex faces of the core n-polytope (equilateral triangles for the great icosahedron, and line segments for the pentagram) until the figure regains regular faces. The grand 600-cell can be seen as its four-dimensional analogue using the same process.