Gyroelongated square cupola
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Gyroelongated square cupola | |
---|---|
Rank | 3 |
Type | CRF |
Notation | |
Bowers style acronym | Gyescu |
Coxeter diagram | oxo8sox&#xt |
Elements | |
Faces | 4+4+4+8 triangles, 1+4 squares, 1 octagon |
Edges | 4+4+4+8+8+8+8 |
Vertices | 4+4+4+8 |
Vertex figures | 4 isosceles trapezoids, edge lengths 1, √2, √2, √2 |
8 irregular pentagons, edge lengths 1, 1, 1, 1, √2 | |
8 isosceles trapezoids, edge lengths 1, 1, 1, √2+√2 | |
Measures (edge length 1) | |
Volume | |
Dihedral angles | 3–3 antiprismatic: |
3–3 join: | |
3–4 cupolaic: | |
3–4 join: | |
4–4: 135° | |
3–8: | |
Central density | 1 |
Number of external pieces | 26 |
Level of complexity | 22 |
Related polytopes | |
Army | Gyescu |
Regiment | Gyescu |
Dual | Tetradeltoctapentagonal hemitrapezohedron |
Conjugate | Gyroelongated retrograde square cupola |
Abstract & topological properties | |
Flag count | 176 |
Euler characteristic | 2 |
Surface | Sphere |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | B2×I, order 8 |
Convex | Yes |
Nature | Tame |
The gyroelongated square cupola is one of the 92 Johnson solids (J23). It consists of 4+4+4+8 triangles, 1+4 squares, and 1 octagon. It can be constructed by attaching an octagonal antiprism to the octagonal base of the square cupola.
If a second cupola is attached to the other octagonal base of the antiprism, the result is the gyroelongated square bicupola.
Vertex coordinates[edit | edit source]
A gyroelongated square cupola of edge length 1 has the following vertices:
where is the distance between the octagonal antiprism's center and the center of one of its bases.
External links[edit | edit source]
- Klitzing, Richard. "gyescu".
- Quickfur. "The Gyroelongated Square Cupola".
- Wikipedia contributors. "Gyroelongated square cupola".
- McCooey, David. "Gyroelongated Square Cupola"