The naming of individual polyhedra is discussed
on its own separate page.

**antiprism** - A semi-regular polyhedron constructed from two *n-sided*
polygons and 2*n* triangles. See the prisms
and antiprisms entry.

**Archimedean** - The 13 Archimedean
solids are convex semi-regular polyhedra.

**canonical form - **A form of any given polyhedron distorted so
every edge is tangent to the unit sphere and the center of gravity of the
tangent points is the origin. See the canonical
form page.

**chiral** - Having different left-handed and right-handed forms;
not mirror symmetric; opposite of *reflexible*. The cube is not chiral;
the snub cube is chiral as these two
versions of the snub cube illustrate.

**compound **- An assemblage of two
or more polyhedra, usually interpenetrating and having a common center.

**convex** - A convex polygon or polyhedron contains no holes or
indentions. If one constructs a line segment between any two points of
a convex object, then every point on the line segment is part of the object.
The pentagram is a non-convex polygon; the
Kepler-Poinsot solids are non-convex
polyhedra.

**dihedral angle** - The angle defined by two given faces meeting
at an edge, e.g., all the dihedral angles of a cube are 90 degrees. An
almost-spherical polyhedron (with many faces) has small dihedral angles.

**edge** - A line segment where two faces meet. A cube has 12 edges.

**enantiomorph** - the mirror image of a given chiral polyhedron.

**face** - A polygon bounding a polyhedron. A cube has six square
faces.

**golden ratio** - (1+sqrt(5))/2, approximately 1.61803, which happens
to be the ratio of a diagonal of a pentagon to its side. This constant
shows up in many metrical properties of the dodecahedron and icosahedron
just as the square root of 2 shows up in the metrical properties of the
cube. A **golden rectangle** has sides in this ratio. A **golden rhombus**
has diagonals in this ratio.

**net **- a drawing of a polyhedron unfolded along its edges, to
lay flat in a plane. The earliest known examples of nets to represent polyhedra
are by Albrecht Durer.

**pentagram** - five-pointed star.

**Platonic** - Five fundamental convex
polyhedra. They have regular faces and identical vertices.

**polygon** - A connected two-dimensional
figure bounded by line segments, called sides, with exactly two sides
meeting at each vertex.

**polyhedron** - A three dimensional object bounded by polygons,
with each edge shared by exactly two polygons. Various authors differ on
the fine points of the definition, e.g., whether it is a solid or just
the surface, whether it can be infinite, and whether it can have two different
vertices that happen to be at the same location.

**prism** - A semi-regular polyhedron constructed from two *n-sided*
polygons and *n* squares. See the prisms
and antiprisms entry.

**quasi-regular** - The edge-regular polyhedra within the uniform
solids having special properties.

**reflexible** - Having a plane of mirror symmetry; opposite of *chiral*.

**regular** - A polygon is regular if
its sides are equal and its angles are equal. A polyhedron is regular if
every face is regular and if every vertex figure is regular. Standardly,
there are nine regular polyhedra: the five
Platonic solids and the four Kepler-Poinsot
solids, but others might be allowed, depending on the definition of
polyhedron.

**rhombus -** A polygon consisting of four equal sides, e.g., in
zonohedra.

**self-intersecting - **A polygon with edges
which cross other edges; a polyhedron
with faces which cross other faces.

**semi-regular** - Consisting of two or more types of regular polygons,
with all vertices identical. This includes the Archimedean
solids, the prisms and antiprisms, and
the nonconvex uniform solids.

**stellation** - The process of constructing
a new polyhedron by extending the face planes of a given polyhedron past
their edges. See, e.g., the 59
stellations of the icosahedron.

**truncate **- To slice off a corner of a polyhedron around a vertex.
The figure at the top of this page shows a cube with one vertex truncated.

**uniform** - A uniform polyhedron has regular faces, with each vertex
equivalently arranged. This includes the Platonic
solids, the Archimedean solids,
the prisms and antiprisms, and the nonconvex
uniform solids.

**vertex** - A point at which edges meet. A cube has 8 vertices.

**vertex figure** - The polygon which appears if one truncates a
polyhedron at a vertex. The figure at the top of this page shows that the
vertex figure of the cube is the equilateral triangle. To be sure to be
consistent, one can truncate at the midpoints of the edges.

**zonohedron -** A polyhedron in which
the faces are all parallelograms or parallel-sided.