Hexagonal antiprism

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.

Uniform hexagonal antiprism

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
Symmetry group	D_6d, [2⁺,12], (2*6), order 24
Rotation group	D₆, [6,2]⁺, (622), order 12
References	U_77(d)
Dual	Hexagonal trapezohedron
Properties	convex
Vertex figure 3.3.3.6

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 $.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}180°/n$ . 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, $2 n$ isosceles triangles.

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

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