In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the pentagonal orthobirotunda is one of the Johnson solid

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...

s (J₃₄). As the name suggests, it can be constructed by joining two pentagonal rotunda

Pentagonal rotunda

In geometry, the pentagonal rotunda is one of the Johnson solids . It can be seen as half an icosidodecahedron.The 92 Johnson solids were named and described by Norman Johnson in 1966.-Formulae:...

e (J₆) along their decagon

Decagon

In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and each internal angle equal to 144°...

al faces, matching like faces. A 36-degree rotation of one rotunda before the joining, so that pentagons abut triangles and vice versa, yields an icosidodecahedron

Icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon...

, one of the Archimedean solid

Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...

s.

The 92 Johnson solids were named and described by Norman Johnson in 1966.