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The stella octangula, also known as the stellated octahedron, Star Tetrahedron, eight-pointed star, or two-dimensionally
2D geometric model

A 2D geometric model is a geometric model of an object as two-dimensional figure, usually on the Euclidean plane or Cartesian plane.Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, such as paper cut-outs and machine parts made of sheet metal....
 as the Star of David
Star of David

The Star of David or Shield of David is a generally recognized symbol of Jewish identity and Judaism.It is named after King David of History of ancient Israel and Judah; and its earliest known communal usage began in the Middle Ages, alongside the more ancient symbol of the Menorah ....
. It was given its name by Johannes Kepler
Johannes Kepler

Johannes Kepler was a Germans mathematician, astronomer and astrologer, and key figure in the 17th century Scientific revolution. He is best known for his eponymous Kepler's laws of planetary motion, codified by later astronomers based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astrononomy....
 in 1609, though it was known to earlier geometers. It was first depicted in Pacioli's Divina Proportione, 1509.

It is the simplest of five regular polyhedral compound
Polyhedral compound

A polyhedral compound is a polyhedron that is itself composed of several other polyhedra sharing a common centre. They are the three-dimensional analogs of star polygon#Star figuress such as the hexagram....
s.

It can be seen as either a polyhedron compound or 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....
:

As a compound, is constructed as the union of two tetrahedra
Tetrahedron

A tetrahedron is a polyhedron composed of four triangle faces, three of which meet at each vertex . A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids....
 (a tetrahedron and its counter-tetrahedron).






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The stella octangula, also known as the stellated octahedron, Star Tetrahedron, eight-pointed star, or two-dimensionally
2D geometric model

A 2D geometric model is a geometric model of an object as two-dimensional figure, usually on the Euclidean plane or Cartesian plane.Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, such as paper cut-outs and machine parts made of sheet metal....
 as the Star of David
Star of David

The Star of David or Shield of David is a generally recognized symbol of Jewish identity and Judaism.It is named after King David of History of ancient Israel and Judah; and its earliest known communal usage began in the Middle Ages, alongside the more ancient symbol of the Menorah ....
. It was given its name by Johannes Kepler
Johannes Kepler

Johannes Kepler was a Germans mathematician, astronomer and astrologer, and key figure in the 17th century Scientific revolution. He is best known for his eponymous Kepler's laws of planetary motion, codified by later astronomers based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astrononomy....
 in 1609, though it was known to earlier geometers. It was first depicted in Pacioli's Divina Proportione, 1509.

It is the simplest of five regular polyhedral compound
Polyhedral compound

A polyhedral compound is a polyhedron that is itself composed of several other polyhedra sharing a common centre. They are the three-dimensional analogs of star polygon#Star figuress such as the hexagram....
s.

It can be seen as either a polyhedron compound or 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....
:

As a compound, is constructed as the union of two tetrahedra
Tetrahedron

A tetrahedron is a polyhedron composed of four triangle faces, three of which meet at each vertex . A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids....
 (a tetrahedron and its counter-tetrahedron). The 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....
 of the two tetrahedra is shared by a cube. The intersection of the two tetrahedra form an inner octahedron
Octahedron

An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each wikt:vertex....
, which shares the same face-planes as the compound.

It can be seen as an octahedron
Octahedron

An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each wikt:vertex....
 with tetrahedral pyramids
Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex . Each base edge and apex form a triangle....
 on each face. It has the same topology as the convex Catalan solid
Catalan solid

In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. The Catalan solids are named for the Belgium mathematician, Eug?ne Catalan, who first described them in 1865....
, the triakis octahedron
Triakis octahedron

A triakis octahedron is an Archimedean solid solid, or a Catalan solid. Its dual is the truncated cube.It can be seen as an octahedron with Tetrahedron added to each face, and is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron....
, which has much shorter pyramids.

As 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....
, it is the only stellated form of the octahedron
Octahedron

An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each wikt:vertex....
. The stellation facets are very simple:
Stellation of Octahedron Facets
(See Wenninger model W19
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....
.)

See also

  • Polyhedron
    Polyhedron

    |}A polyhedron is often defined as a geometry object with flat faces and straight edges .This definition of a polyhedron is not very precise, and to a modern mathematician is quite unsatisfactory....
  • Merkaba
  • Polyhedron model
    Polyhedron model

    A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material....
    s
  • Plane (metaphysics)
    Plane (metaphysics)

    In metaphysics and esoteric cosmology, a plane, other than the physical plane is conceived as a subtle state of consciousness that Transcendence the known physical universe....


External links

  • VRML
    VRML

    VRML is a standard file format for representing 3-D computer graphics interactive vector graphics, designed particularly with the World Wide Web in mind....
     model: