geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, the great stellapentakis dodecahedron (or great astropentakis dodecahedron) is a nonconvex

isohedral In geometry, a tessellation of dimension (a plane tiling) or higher, or a polytope of dimension (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same. More specifically, all faces must be not merely congruen ...

polyhedron In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal Face (geometry), faces, straight Edge (geometry), edges and sharp corners or Vertex (geometry), vertices. The term "polyhedron" may refer ...

. It is the dual of the truncated great icosahedron. It has 60 intersecting triangular faces.

Proportions

The triangles have one angle of

\arccos(-\frac-\frac\sqrt)\approx 138.891\,114\,686\,59^

and two of

\arccos(\frac+\frac\sqrt)\approx 20.554\,442\,656\,71^

. The dihedral angle equals

\arccos(\frac)\approx 123.320\,065\,258\,47^

. Part of each triangle lies within the solid, hence is invisible in solid models.

References

External links

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Uniform polyhedra and duals
Dual uniform polyhedra {{polyhedron-stub