The Gyroelongated Pentagonal Pyramid
The gyroelongated pentagonal pyramid is the 11th Johnson solid (J11). It has 11 vertices, 25 edges, and 16 faces (15 equilateral triangles and 1 pentagon).
The gyroelongated pentagonal pyramid can be constructed by attaching a pentagonal pyramid to a pentagonal antiprism. It can also be constructed by deleting a single vertex from the icosahedron, and so can also be called the monodiminished icosahedron. It can be further diminished by removing a vertex not opposite the pentagonal face, producing a metabidiminished icosahedron (J62), or by removing two vertices, producing a tridiminished icosahedron (J63).
Here are some views of the gyroelongated pentagonal pyramid from various angles:
The Cartesian coordinates of the gyroelongated pentagonal pyramid with edge length 2 are:
- (0, 0, √((5+√5)/2))
- ±(B, 0, A)
- ±(C, ±φ, A)
- ±(−D, ±1, A)