Hexagonal antiprismatic prism
Jump to navigation
Jump to search
Hexagonal antiprismatic prism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Happip |
Coxeter diagram | x2s2s12o () |
Elements | |
Cells | 12 triangular prisms, 2 hexagonal prisms, 2 hexagonal antiprisms |
Faces | 24 triangles, 12+12 squares, 4 hexagons |
Edges | 12+24+24 |
Vertices | 24 |
Vertex figure | Isosceles trapezoidal pyramid, edge lengths 1, 1, 1, √3 (base), √2 (legs) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Trip–4–trip: |
Trip–4–hip: | |
Hap–6–hip: 90° | |
Hap–3–trip: 90° | |
Heights | Hap atop hap: 1 |
Hip atop gyro hip: | |
Central density | 1 |
Number of external pieces | 16 |
Level of complexity | 16 |
Related polytopes | |
Army | Happip |
Regiment | Happip |
Dual | Hexagonal antitegmatic tegum |
Conjugate | Hexagonal antiprismatic prism |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | (I2(12)×A1)+×A1, order 48 |
Convex | Yes |
Nature | Tame |
The hexagonal antiprismatic prism or happip is a prismatic uniform polychoron that consists of 2 hexagonal antiprisms, 2 hexagonal prisms, and 12 triangular prisms. Each vertex joins 1 hexagonal antiprism, 1 hexagonal prism, and 3 triangular prisms. As the name suggests, it is a prism based on a hexagonal antiprism. It is also a CRF segmentochoron designated K-4.53 on Richard Klitzing's list.
Vertex coordinates[edit | edit source]
The vertices of a hexagonal antiprismatic prism of edge length 1 are given by:
Representations[edit | edit source]
A hexagonal antiprismatic prism has the following Coxeter diagrams:
- x2s2s12o (full symmetry)
- x2s2s6s ()
- xx xo6ox&#x (hexagonal prism atop gyrated hexagonal prism)
External links[edit | edit source]
- Bowers, Jonathan. "Category B: Antiduoprisms".
- Klitzing, Richard. "happip".
- Wikipedia contributors. "Uniform antiprismatic prism".