Hexagonal antiprism

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Uniform Hexagonal antiprism
Hexagonal antiprism.png
Type Prismatic uniform polyhedron
Elements F = 14, E = 24
V = 12 (χ = 2)
Faces by sides 12{3}+2{6}
Schläfli symbol s{2,12}
sr{2,6}
Wythoff symbol | 2 2 6
Coxeter diagram CDel node h.pngCDel 2x.pngCDel node h.pngCDel 12.pngCDel node.png
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 6.pngCDel node h.png
Symmetry group D6d, [2+,12], (2*6), order 24
Rotation group D6, [6,2]+, (622), order 12
References U77(d)
Dual Hexagonal trapezohedron
Properties convex
Hexagonal antiprism vertfig.png
Vertex figure
3.3.3.6

In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

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 6-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.

Related polyhedra[edit]

The hexagonal faces can be replaced by coplanar triangles, leading to a nonconvex polyhedron with 24 equilateral triangles.

Augmented hexagonal antiprism flat.png

External links[edit]