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 parabidiminished rhombicosidodecahedron is one of the

Johnson solid In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two Solid geometry, s ...

s (). It is also a

canonical polyhedron In geometry, the midsphere or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform polyhedra, including the regular, quasiregular and semiregul ...

. It can be constructed as a

rhombicosidodecahedron In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has a total of 62 faces: 20 regular triangular faces, 30 square f ...

with two opposing pentagonal cupolae removed. Related Johnson solids are the diminished rhombicosidodecahedron () where one cupola is removed, the metabidiminished rhombicosidodecahedron () where two non-opposing cupolae are removed, and the tridiminished rhombicosidodecahedron () where three cupolae are removed.

Example

External links

* Johnson solids {{Polyhedron-stub