Icosahedron

In geometry, an icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a special polyhedron with 20 faces. The name comes from Ancient Greek, where "εἴκοσι" means "twenty" and "ἕδρα" means "seat."

The most famous type is the regular icosahedron. This shape is one of the Platonic solids, which are perfectly symmetrical 3D shapes. The regular icosahedron has 20 faces, and each face is an equilateral triangle, meaning all three sides of each triangle are the same length.

The regular icosahedron is beautiful and useful. It appears in the structure of some viruses and in the design of scientific instruments. Learning about shapes like the icosahedron helps us understand the world better.

Regular icosahedra

Main articles: Regular icosahedron and Great icosahedron

An icosahedron is a special shape in geometry. It has 20 triangular faces and 30 edges. There are two main types. One type is convex, meaning all its faces curve outward. The other type is non-convex and is called the great icosahedron. Both types have the same symmetry. When people talk about a regular icosahedron, they usually mean the convex one. This shape is also a type of Platonic solid.

Pyritohedral icosahedra

A regular icosahedron can change shape but still keep some of its symmetry. This makes a shape called a snub octahedron or pseudo-icosahedron. These shapes have 8 equilateral triangles and 12 isosceles triangles instead of 20 equilateral triangles.

The points of these changed shapes can be described using special math rules. These shapes are related to other polyhedra like the cuboctahedron and form a group of related shapes.

Other icosahedra

Other icosahedra come in many shapes. Some are regular, and others are not.

One example is Jessen's icosahedron. It has eight equilateral triangles and twelve isosceles triangles.

You can also find icosahedra shaped like pyramids, prisms, and antiprisms. Some special shapes include the gyroelongated triangular cupola and the triangular hebesphenorotunda.