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Hexagonal Antiprism: Interactive Polyhedron model
www.georgehart.com: The Encyclopedia of Polyhedra ** VRMLbr>model
polyhedronisme
A6 Prismatoid polyhedra {{Polyhedron-stub
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, 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
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...
caps.
Antiprisms are similar to prism
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentary ...
s 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 6-sided base, one usually considers the case where its copy is twisted by an angle . 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 bases and, connecting those bases, isosceles triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter versio ...
s.
If faces are all regular, it is a semiregular polyhedron
In geometry, the term semiregular polyhedron (or semiregular polytope) is used variously by different authors.
Definitions
In its original definition, it is a polyhedron with regular polygonal faces, and a symmetry group which is transitive on ...
.
Crossed antiprism
A crossed hexagonal antiprism is a star polyhedron, topologically identical to the convex ''hexagonal antiprism'' with the same vertex arrangement, but it can't be made uniform; the sides areisosceles triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter versio ...
s. Its vertex configuration is 3.3/2.3.6, with one triangle retrograde. It has D6d symmetry, order 24.
:
Related polyhedra
The hexagonal faces can be replaced by coplanar triangles, leading to a nonconvex polyhedron with 24 equilateral triangles. :
External links
*Hexagonal Antiprism: Interactive Polyhedron model
www.georgehart.com: The Encyclopedia of Polyhedra ** VRMLbr>model
polyhedronisme
A6 Prismatoid polyhedra {{Polyhedron-stub