Elongated pentagonal cupola
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| Elongated pentagonal cupola | |
|---|---|
 | |
| Type | Johnson J19 – J20 – J21 |
| Faces | 5 triangles 15 squares 1 pentagon 1 decagon |
| Edges | 45 |
| Vertices | 25 |
| Vertex configuration | 10(42.10) 10(3.43) 5(3.4.5.4) |
| Symmetry group | C5v |
| Properties | convex, composite |
| Net | |
 | |
The elongated pentagonal cupola is a polyhedron, constructed by attaching pentagonal cupola to a decagonal prism to its base. It is a Johnson solid.
The elongated pentagonal cupola is constructed from a ten-sided prism by attaching a pentagonal cupola onto one of its bases, a process known as elongation. This cupola covers one of the prism's two decagons, so that the resulting polyhedron has five equilateral triangles, fifteen squares, one regular pentagon, and one regular decagon.[1] Because of this construction, the elongated pentagonal cupola is composite. A convex polyhedron in which all of the faces are regular polygons is called a Johnson solid. The elongated pentagonal cupola is one of them, enumerated as the twentieth Johnson solid .[2]
