Octagonal antifastegium |
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Rank | 4 |
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Type | Segmentotope |
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Notation |
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Bowers style acronym | Oaf |
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Coxeter diagram | ox xo8ox&#x |
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Elements |
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Cells | 8 tetrahedra, 8 square pyramids, 1 octagonal prism, 2 octagonal antiprisms |
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Faces | 16+16+16 triangles, 8 squares, 1+2 octagons |
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Edges | 8+8+16+32 |
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Vertices | 8+16 |
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Vertex figures | 8 wedges, edge lengths √2+√2 (top) and 1 (remaining edges) |
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| 16 isosceles trapezoidal pyramids, base edge lengths 1, 1, 1, √2+√2, side edge lengths 1, 1, √2, √2 |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | ≈ 1.73655 |
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Dichoral angles | Tet–3–squippy: |
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| Op–4–squippy: |
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| Oap–3–tet: |
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| Oap–3–squippy: |
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| Oap–8–oap: |
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| Op–8–oap: |
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Heights | Oc atop oap: |
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| Oc atop gyro op: |
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Central density | 1 |
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Related polytopes |
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Army | Oaf |
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Regiment | Oaf |
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Dual | Octagonal antitegmatonotch |
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Conjugate | Octagrammic antifastegium |
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Abstract & topological properties |
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Euler characteristic | 0 |
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Orientable | Yes |
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Properties |
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Symmetry | I2(8)×A1×I, order 32 |
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Convex | Yes |
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Nature | Tame |
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The octagonal antifastegium, or oaf, is a CRF segmentochoron (designated K-4.58 on Richard Klitzing's list). It consists of 1 octagonal prism, 2 octagonal antiprisms, 8 tetrahedra, and 8 square pyramids. It is a member of the infinite family of polygonal antifastegiums.
It is a segmentochoron between an octagon and an octagonal antiprism or between an octagon and a gyro octagonal prism.
The vertices of an octagonal antifastegium of edge length 1 are given by:
The octagonal antifastegium can be represented by the following Coxeter diagrams:
- Klitzing, Richard. "oaf".