Heptagonal antiprism

Uniform heptagonal antiprism
Type	Prismatic uniform polyhedron
Elements	F = 16, E = 28 V = 14 (χ = 2)
Faces by sides	14{3}+2{7}
Schläfli symbol	s{2,14} sr{2,7}
Wythoff symbol	| 2 2 7
Coxeter diagram
Symmetry group	D7d, [2+,14], (2*7), order 28
Rotation group	D7, [7,2]+, (722), order 14
References	U77(e)
Dual	Heptagonal trapezohedron
Properties	convex
Vertex figure 3.3.3.7

In geometry, the heptagonal antiprism is the fifth 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 7-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[]

Family of uniform n-gonal antiprisms

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Antiprism name	Digonal antiprism	(Trigonal) Triangular antiprism	(Tetragonal) Square antiprism	Pentagonal antiprism	Hexagonal antiprism	Heptagonal antiprism	Octagonal antiprism	Enneagonal antiprism	Decagonal antiprism	Hendecagonal antiprism	Dodecagonal antiprism	...	Apeirogonal antiprism
Polyhedron image												...
Spherical tiling image												Plane tiling image
Vertex config.	2.3.3.3	3.3.3.3	4.3.3.3	5.3.3.3	6.3.3.3	7.3.3.3	8.3.3.3	9.3.3.3	10.3.3.3	11.3.3.3	12.3.3.3	...	∞.3.3.3

External links[]

• Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
  • VRML model
• polyhedronisme A7

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