Pentagonal orthobirotunda
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| Pentagonal orthobirotunda | |
|---|---|
 | |
| Type | Birotunda, Johnson J33 – J34 – J35 |
| Faces | 2×10 triangles 2+10 pentagons |
| Edges | 60 |
| Vertices | 30 |
| Vertex configuration | 10(32.52) 2.10(3.5.3.5) |
| Symmetry group | D5h |
| Properties | convex |
| Net | |
 | |
In geometry, the pentagonal orthobirotunda is a polyhedron constructed by attaching two pentagonal rotundae along their decagonal faces, matching like faces. It is a Johnson solid.
The pentagonal orthobirotunda is constructed by attaching two pentagonal rotundas to their base, covering decagon faces. The resulting polyhedron has 32 faces, 30 vertices, and 60 edges. This construction is similar to icosidodecahedron (or pentagonal gyrobirotunda), an Archimedean solid: the difference is one of its rotundas twisted around 36°, making the pentagonal faces connect to the triangular one, a process known as gyration.[1][2] A convex polyhedron in which all of the faces are regular polygons is the Johnson solid. The pentagonal orthobirotunda is one of them, enumerated as the 34th Johnson solid .[3]
