# Glossary

Here are a few of the words that are used on this site and their meanings.

### ARCHIMEDEAN SOLIDS

Symmetric semi-regular polyhedra made of two or three regular polygons that meet at identical vertices. There are 13 Archimedean solids plus two mirror image forms. They are named for the mathematician Archimedes.

### BUCKYBALL

A simple name for the Buckminsterfullerene molecule, C60. The shape being that of a truncated icosahedron with a carbon atom at each vertex.

### COSINE

The relationship of a right triangle where the cosine gives the ratio of the length of the side adjacent to an angle to the length of the hypotenuse. Cosine of the angle equals the adjacent side length divided by the hypotenuse length.

### DODECAHEDRON

A 12 faced polyhedron, each face consisting of a regular pentagon. A member of the Platonic solids.

### EDGE

The line segments making up a polygon or polyhedron. The line formed by the joining or intersection of the faces of a polyhedron.

### HEXAHEDRON

Another name for a cube, a polyhedron with six faces, each a square. A member of the Platonic solids.

### ICOSAHEDRON

A 20-faced polyhedron, consisting of 20 equilateral triangles, five meeting at each vertex. A member of the Platonic solids.

### N-GON

An n-gon is a polygon with n sides.

### OCTAHEDRON

An eight-faced polyhedron, consisting of eight equilateral triangles, four meeting at each vertex. A member of the Platonic solids.

### PHI

The golden ratio, symbolized by the Greek letter $$\phi$$, in which phi has the unique property $$\phi +1 = \phi^2$$. The formula is $$\phi = \frac12(1+\sqrt5)$$. See here.

### PLATONIC SOLID

A geometric shape made of only one type of regular polygon. There are only five Platonic solids. They are named for the mathematician Plato.

### POLYGON

A plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. An n-gon is a polygon with n sides.

### POLYHEDRON

In elementary geometry a polyhedron (plural polyhedra or polyhedrons) is a geometric solid in three dimensions with flat faces and straight edges.

### SINE

The relationship of a right triangle where the sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse. Sine of the angle equals the opposite side length divided by the hypotenuse length.

### STELLATION

The process of constructing new polygons (in two dimensions), or new polyhedra in three dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way, until they meet each other again. The new figure is a stellation of the original.

### TETRAHEDRON

A four-faced polyhedron, consisting of four equilateral triangles, three meeting at each vertex. A member of the Platonic solids. Also called a regular triangular pyramid.

### TRUNCATED ICOSAHEDRON

A polyhedron with 12 regular pentagonal faces and 20 regular hexagonal faces. Each vertex being the meeting of one pentagon and two hexagons.

Formed by the truncation (cutting off) of a regular pentagonal pyramid from each vertex of an icosahedron, resulting in 12 new pentagonal faces.

Perhaps the best-known example of a spherical polyhedron analog to the truncated icosahedron is the soccer ball.

### VERTEX

The point where one or more line segments join or intersect. Plural is vertices.

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