34 relations: Antiprism, Antiprism graph, Compound of three tetrahedra, Coordination geometry, Deltahedron, Dodecagon, Dodecahedron, Gyroelongated triangular bicupola, Gyroelongated triangular cupola, Hexagon, Hexagonal trapezohedron, Improper rotation, Johnson solid, List of polygons, polyhedra and polytopes, List of small polyhedra by vertex count, List of uniform polyhedra, List of uniform polyhedra by Schwarz triangle, Near-miss Johnson solid, Paracompact uniform honeycombs, Prismatic compound of antiprisms, Prismatic uniform polyhedron, Skew polygon, Snub (geometry), Snub polyhedron, Spherical polyhedron, Square antiprism, Tetradecahedron, Triangular tiling honeycomb, Uniform antiprismatic prism, Uniform polyhedron, VSEPR theory, Wythoff construction, Wythoff symbol, 24-cell.

## 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.

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## Antiprism graph

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

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## 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.

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## Coordination geometry

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

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## Deltahedron

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

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## Dodecagon

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

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## Dodecahedron

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

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## Gyroelongated triangular bicupola

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

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## Gyroelongated triangular cupola

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

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## Hexagon

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

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## 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.

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## Improper rotation

In geometry, an improper rotation,.

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## 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.

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## List of polygons, polyhedra and polytopes

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

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## List of small polyhedra by vertex count

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

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## 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).

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## List of uniform polyhedra by Schwarz triangle

There are many relationships among the uniform polyhedra.

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## 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.

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## Paracompact uniform honeycombs

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

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## Prismatic compound of antiprisms

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

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## Prismatic uniform polyhedron

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

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## Skew polygon

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

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## Snub (geometry)

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

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## Snub polyhedron

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

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## 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.

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## 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.

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## Tetradecahedron

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

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## Triangular tiling honeycomb

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

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## 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.

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## 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).

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## 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.

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## Wythoff construction

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

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## Wythoff symbol

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

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## 24-cell

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

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