Octagonal antiprism

In geometry, the octagonal antiprism is the 6th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

Uniform octagonal antiprism
TypePrismatic uniform polyhedron
ElementsF = 18, E = 32
V = 16 (χ = 2)
Faces by sides16{3}+2{8}
Schläfli symbols{2,16}
sr{2,8}
Wythoff symbol| 2 2 8
Coxeter diagram
Symmetry groupD8d, [2+,16], (2*8), order 32
Rotation groupD8, [8,2]+, (822), order 16
ReferencesU77(f)
DualOctagonal trapezohedron
Propertiesconvex

Vertex figure
3.3.3.8

Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals.

In the case of a regular 8-sided base, one usually considers the case where its copy is twisted by an angle 180°/n. Extra regularity is obtained by the line connecting the base centers being perpendicular to the base planes, making it a right antiprism. As faces, it has the two n-gonal bases and, connecting those bases, 2n isosceles triangles.

If faces are all regular, it is a semiregular polyhedron.

See also

  • Weisstein, Eric W. "Antiprism". MathWorld.
  • Octagonal Antiprism -- Interactive Polyhedron Model
  • Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
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