Introduction

The cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15.
Its vertex figure is a crossed quadrilateral.
A nonconvex polyhedron has intersecting faces which do not represent new edges or faces.

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Introduction

A deltoidal icositetrahedron is a Catalan solid which looks a bit like an overinflated cube.
Its dual polyhedron is the rhombicuboctahedron.

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Introduction

The octahemioctahedron is a nonconvex uniform polyhedron.
Its vertex figure is a crossed quadrilateral.

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Introduction

The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces.
It is an Archimedean dual solid, or a Catalan solid.
Its dual is the cuboctahedron.

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Introduction

A rhombic icosahedron is a polyhedron shaped like an oblate sphere.
The rhombic icosahedron is a zonohedron that is dual to an irregular-faced pentagonal gyrobicupola.

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Introduction

A rhombohedron is a three-dimensional figure like a cube,
except that its faces are not squares but rhombi.
It is a special case of a parallelepiped where all edges are the same length.

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Introduction

The small dodecahemidodecahedron is a nonconvex uniform polyhedron.
Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.
It is a hemipolyhedron with six decagonal faces passing through the model center.

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Introduction

The small dodecahemidodecahedron is a nonconvex uniform polyhedron.
Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.
It is a hemipolyhedron with six decagonal faces passing through the model center.

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Introduction

The truncated icosahedron is an Archimedean solid,
one of thirteen convex isogonal nonprismatic solids whose faces are two or more types of regular polygon.
It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.

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Introduction

A cuboctahedron is a polyhedron with eight triangular faces and six square faces.
A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each,
and 24 identical edges, each separating a triangle from a square.
As such it is a quasiregular polyhedron, i.e. an Archimedean solid,
being vertex-transitive and edge-transitive.
Its dual polyhedron is the rhombic dodecahedron.

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