Octagonal antifastegium

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Octagonal antifastegium
Rank4
TypeSegmentotope
Notation
Bowers style acronymOaf
Coxeter diagramox xo8ox&#x
Elements
Cells8 tetrahedra, 8 square pyramids, 1 octagonal prism, 2 octagonal antiprisms
Faces16+16+16 triangles, 8 squares, 1+2 octagons
Edges8+8+16+32
Vertices8+16
Vertex figures8 wedges, edge lengths 2+2 (top) and 1 (remaining edges)
 16 isosceles trapezoidal pyramids, base edge lengths 1, 1, 1, 2+2, side edge lengths 1, 1, 2, 2
Measures (edge length 1)
Circumradius
Hypervolume≈ 1.73655
Dichoral anglesTet–3–squippy:
 Op–4–squippy:
 Oap–3–tet:
 Oap–3–squippy:
 Oap–8–oap:
 Op–8–oap:
HeightsOc atop oap:
 Oc atop gyro op:
Central density1
Related polytopes
ArmyOaf
RegimentOaf
DualOctagonal antitegmatonotch
ConjugateOctagrammic antifastegium
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(8)×A1×I, order 32
ConvexYes
NatureTame

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.

Vertex coordinates[edit | edit source]

The vertices of an octagonal antifastegium of edge length 1 are given by:

Representations[edit | edit source]

The octagonal antifastegium can be represented by the following Coxeter diagrams:

  • ox xo8ox&#x
  • xoo8oxx&#x

External links[edit | edit source]

  • Klitzing, Richard. "oaf".