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 | |
|---|---|
 | |
| Type | Prismatic uniform polyhedron |
| Elements | F = 26, E = 48 V = 24 (χ = 2) |
| Faces by sides | 24{3}+2{12} |
| Schläfli symbol | s{2,24} sr{2,12} |
| Wythoff symbol | | 2 2 12 |
| Coxeter diagram |      |
| Symmetry group | D12d, [2+,24], (2*12), order 48 |
| Rotation group | D12, [12,2]+, (12.2.2), order 24 |
| References | U77(j) |
| Dual | Dodecagonal trapezohedron |
| Properties | convex |
 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
| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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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
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