Glossary

Archimedean solid: a convex semiregular polyhedron. All faces are regular polygons, but not all faces are the same.

For example, a truncated icosahedron is an Archimedean solid. A soccer ball looks like this polyhedron.

convex: not having indentations. Technically, a polygon or polyhedron is convex when the segment joining any two of its points lies entirely within it.

For example, a pentagon and the regular dodecahedron are convex, but a pentagram and the small stellated dodecahedron are nonconvex.

convex hull: the smallest convex polyhedron including a given polyhedron.

For example, the convex hull of the small stellated dodecahedron is the regular icosahedron.

cube: the Platonic solid having six square faces. It is also called the hexahedron.

dodecahedron: a polyhedron having twelve faces.

Euler's formula: the formula V - E + F = 2 relating the number of vertices, edges, and faces on a convex polyhedron.

great dodecahedron: a nonconvex regular polyhedron having twelve pentagons for faces. It is one of the four Kepler-Poinsot polyhedra.

irregular dodecahedron: a dodecahedron whose faces are irregular polygons.

net: a layout of polygons which may be folded to obtain a polyhedron.

nonconvex: having indentations. Technically, a polygon or polyhedron is nonconvex if there is a segment joining two of its points, part of which lies outside the polygon or polyhedron.

For example, a pentagram and the small stellated dodecahedron are nonconvex.

pentagonal dodecahedron: a dodecahedron with pentagonal faces.

Platonic solid: one of the five convex regular polyhedra.

polytope: generic name for a polygon or polyhedron in four or more dimensions.

rhombic dodecahedron: a dodecahedron whose faces are rhombi.

rhombus: a quadrilateral whose four sides all have the same length.

small stellated dodecahedron: a nonconvex regular polyhedron having twelve pentagrams for faces. It is one of the four Kepler-Poinsot polyhedra.

tetravalent vertex: a vertex of a polyhedron where four faces meet. Four edges also meet at such a vertex.

trivalent vertex: a vertex of a polyhedron where three faces meet. Three edges also meet at such a vertex.

vertex: a corner of a polygon or polyhedron.