Heptagonal antiprism

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Uniform heptagonal antiprism
Antiprism 7.png
Type Prismatic uniform polyhedron
Elements F = 16, E = 28
V = 14 (χ = 2)
Faces by sides14{3}+2{7}
Schläfli symbol s{2,14}
sr{2,7}
Wythoff symbol | 2 2 7
Coxeter diagram CDel node h.pngCDel 2x.pngCDel node h.pngCDel 14.pngCDel node.png
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 7.pngCDel node h.png
Symmetry group D7d, [2+,14], (2*7), order 28
Rotation group D7, [7,2]+, (722), order 14
References U 77(e)
Dual Heptagonal trapezohedron
Properties convex
Heptagonal antiprism vertfig.png
Vertex figure
3.3.3.7

In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by two parallel polygons separated by a strip of triangles. In the case of the heptagonal antiprism, the caps are two regular heptagons. Consequently, this polyhedron features 14 vertices and 14 equilateral triangular faces. There are 14 edges where a triangle meets a heptagon, and an additional 14 edges where two triangles meet.

The heptagonal antiprism was first illustrated by Johannes Kepler as an example of the general construction of antiprisms. [1]

3D model of a uniform heptagonal antiprism Heptagonal antiprism.stl
3D model of a uniform heptagonal antiprism

References

  1. Kepler, Johannes (1619), "Book II, Definition X", Harmonices Mundi (in Latin), p. 49 See also illustration A, of a heptagonal antiprism.