Dodecagonal antiprism

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

Uniform dodecagonal antiprism
TypePrismatic uniform polyhedron
ElementsF = 26, E = 48
V = 24 (χ = 2)
Faces by sides24{3}+2{12}
Schläfli symbols{2,24}
sr{2,12}
Wythoff symbol| 2 2 12
Coxeter diagram
Symmetry groupD12d, [2+,24], (2*12), order 48
Rotation groupD12, [12,2]+, (12.2.2), order 24
ReferencesU77(j)
DualDodecagonal trapezohedron
Propertiesconvex

Vertex figure
3.3.3.12

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 12-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

  • Weisstein, Eric W. "Antiprism". MathWorld.
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