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# Hexagonal antiprism

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. [1]

## Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

## Antiprism graph

In the mathematical field of graph theory, an antiprism graph is a graph that has one of the antiprisms as its skeleton.

## Compound of three tetrahedra

In geometry, a compound of three tetrahedra can be constructed by three tetrahedra rotated by 60 degree turns along an axis of the middle of an edge.

## Coordination geometry

The term coordination geometry is used in a number of related fields of chemistry and solid state chemistry/physics.

## Deltahedron

In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles.

## Dodecagon

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

## Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

## Gyroelongated triangular bicupola

In geometry, the gyroelongated triangular bicupola is one of the Johnson solids (J44).

## Gyroelongated triangular cupola

In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22).

## Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

## Hexagonal trapezohedron

The hexagonal trapezohedron or deltohedron is the fourth in an infinite series of face-uniform polyhedra which are dual polyhedron to the antiprisms.

## Improper rotation

In geometry, an improper rotation,.

## Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism, or antiprism), and each face of which is a regular polygon.

## List of polygons, polyhedra and polytopes

A polytope is a geometric object with flat sides, which exists in any general number of dimensions.

## List of small polyhedra by vertex count

In geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges.

## List of uniform polyhedra

In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

## List of uniform polyhedra by Schwarz triangle

There are many relationships among the uniform polyhedra.

## Near-miss Johnson solid

In geometry, a near-miss Johnson solid is a strictly convex polyhedron whose faces are close to being regular polygons but some or all of which are not precisely regular.

## Paracompact uniform honeycombs

In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells.

## Prismatic compound of antiprisms

In geometry, a prismatic compound of antiprism is a category of uniform polyhedron compound.

## Prismatic uniform polyhedron

In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry.

## Skew polygon

In geometry, a skew polygon is a polygon whose vertices are not all coplanar.

## Snub (geometry)

In geometry, a snub is an operation applied to a polyhedron.

## Snub polyhedron

A snub polyhedron is a polyhedron obtained by alternating a corresponding omnitruncated or truncated polyhedron, depending on the definition.

## Spherical polyhedron

In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

## Square antiprism

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

A tetradecahedron with ''D2d'' symmetry, existing in the Weaire–Phelan structure A tetradecahedron is a polyhedron with 14 faces.

## Triangular tiling honeycomb

The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.

## Uniform antiprismatic prism

In 4-dimensional geometry, a uniform antiprismatic prism or antiduoprism is a uniform 4-polytope with two uniform antiprism cells in two parallel 3-space hyperplanes, connected by uniform prisms cells between pairs of faces.

## Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

## VSEPR theory

Valence shell electron pair repulsion (VSEPR) theory is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms.

## Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

## Wythoff symbol

In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.

## 24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

## References

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