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Uniform dodecagonal antiprism | |
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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 | U 77(j) |
Dual | Dodecagonal trapezohedron |
Properties | convex |
Vertex figure 3.3.3.12 |
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.
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.
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 |
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies of an n-sided polygon, connected by an alternating band of 2ntriangles.
A (symmetric) n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base. An n-gonal bipyramid has 2n triangle faces, 3n edges, and 2 + n vertices.
In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides (J1); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform before they refer to it as a “Johnson solid”.
In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases; example: a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids.
An n-gonal trapezohedron, antidipyramid, antibipyramid, or deltohedron is the dual polyhedron of an n-gonal antiprism. The 2n faces of an n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites.
In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one solid.
In geometry of 4 dimensions or higher, a duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher. The Cartesian product of an n-polytope and an m-polytope is an (n+m)-polytope, where n and m are 2 (polygon) or higher.
In geometry, the square antiprism is the second in an infinite family of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an anticube.
In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
In geometry, the octagonal antiprism is the 6th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with polygonal base. A pyramid with an n-sided base has n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual.
In geometry, a bicupola is a solid formed by connecting two cupolae on their bases.
A snub polyhedron is a polyhedron obtained by alternating a corresponding omnitruncated or truncated polyhedron, depending on the definition. Some but not all authors include antiprisms as snub polyhedra, as they are obtained by this construction from a degenerate "polyhedron" with only two faces.
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.
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.
In geometry, the enneagonal antiprism is one in an infinite set of convex antiprisms formed by triangle sides and two regular polygon caps, in this case two enneagons.
In geometry, the hendecagonal antiprism is the ninth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
In geometry, the dodecagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two dodecagrams.
In geometry, the dodecagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two dodecagrams.