Great stellated dodecahedron

Great Stellated Dodecahedron

	Email		Print
	Bookmark		Link

Great stellated dodecahedron

In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, the great stellated dodecahedron is a Kepler-Poinsot polyhedron. It is one of four nonconvex regular polyhedra.

It is composed of 12 intersecting pentagram

Pentagram

A pentagram is the shape of a five-pointed star drawn with five straight strokes. The word pentagram comes from the Greek language word pe?t???a???? , a noun form of pe?t???a???? or pe?t???a???? , a word meaning roughly "five-lined" or "five lines"....
mic faces, with three pentagrams meeting at each vertex.

It shares its vertex arrangement

Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....
with the regular dodecahedron

Dodecahedron

A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex....
, as well as being a stellation

Stellation

Stellation is a process of constructing new polygons , new polyhedron in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way, until they meet each other again....
of a (smaller) dodecahedron. It is the only dodecahedral stellation with this property, apart from the dodecahedron itself.

Discussion

Ask a question about 'Great stellated dodecahedron'

Start a new discussion about 'Great stellated dodecahedron'

Answer questions from other users

Full Discussion Forum

Encyclopedia

In geometry

Geometry

Pentagram

Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....
with the regular dodecahedron

Dodecahedron

Stellation

Great icosahedron

In geometry, the great icosahedron is a Kepler-Poinsot polyhedra. It is one of four nonconvex regular polyhedra. It is composed of 20 intersecting triangular faces, with five triangles meeting at each vertex in a pentagrammic sequence....
, is related in a similar fashion to the icosahedron

Icosahedron

In geometry, an icosahedron isany polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral triangle s as faces....
.

Shaving the triangular pyramids off results in an icosahedron

Icosahedron

In geometry, an icosahedron isany polyhedron having 20 faces, but usually a regular icosahedron is implied, which has equilateral triangle s as faces....
.

If the pentagrammic faces are broken into triangles, it is topologically related to the triakis icosahedron

Triakis icosahedron

A triakis icosahedron is an Archimedean solid solid, or a Catalan solid. Its dual is the truncated dodecahedron.It can be seen as an icosahedron with Tetrahedron augmented to each face....
, with the same face connectivity, but much taller isosceles triangle faces.

Transparent great stellated dodecahedron (Animation)

As a stellation

It can also be constructed as the third of three stellation

Stellation

Stellation is a process of constructing new polygons , new polyhedron in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way, until they meet each other again....
s of the dodecahedron, and referenced as Wenninger model [W22

List of Wenninger polyhedron models

This table contains an indexed list of the Uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger.The book was written as a guide book to building polyhedra as physical models....
].

The stellation facets for construction are:

Net

The net of a great stellated dodecahedron looks somewhat like this:

Fold forward on the short lines, and backwards on the long lines.

Great stellated dodecahedron

As a stellation

Net

External links