Decagonal antiprism

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Uniform decagonal antiprism
Decagonal antiprism.png
Type Prismatic uniform polyhedron
Elements F = 22, E = 40
V = 20 (χ = 2)
Faces by sides 20{3}+2{10}
Schläfli symbol s{2,20}
sr{2,10}
Wythoff symbol | 2 2 10
Coxeter diagram CDel node h.pngCDel 2x.pngCDel node h.pngCDel 2x.pngCDel 0x.pngCDel node.png
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 10.pngCDel node h.png
Symmetry group D10d, [2+,20], (2*10), order 40
Rotation group D10, [10,2]+, (10.2.2), order 20
References U77(h)
Dual Decagonal trapezohedron
Properties convex
Decagonal antiprism vf.png
Vertex figure
3.3.3.10

In geometry, the decagonal antiprism is the eighth 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 10-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
  • v
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 Digonal antiprism.png Trigonal antiprism.png Square antiprism.png Pentagonal antiprism.png Hexagonal antiprism.png Antiprism 7.png Octagonal antiprism.png Enneagonal antiprism.png Decagonal antiprism.png Hendecagonal antiprism.png Dodecagonal antiprism.png ...
Spherical tiling image Spherical digonal antiprism.png Spherical trigonal antiprism.png Spherical square antiprism.png Spherical pentagonal antiprism.png Spherical hexagonal antiprism.png Spherical heptagonal antiprism.png Spherical octagonal antiprism.png Plane tiling image Infinite antiprism.svg
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[]

  • Weisstein, Eric W. "Antiprism". MathWorld.
  • Decagonal Antiprism: 3-d polyhedron model
  • Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
  • polyhedronisme A10
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