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The stellation diagram for the regular dodecahedron with the central pentagon highlighted. This diagram represents the dodecahedron face itself.
In geometry, a stellation diagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other face planes intersect with this one. The lines cause 2D space to be divided up into regions. Regions not intersected by any further lines are called elementary regions. Usually unbounded regions are excluded from the diagram, along with any portions of the lines extending to infinity. Each elementary region represents a top face of one cell, and a bottom face of another.
A collection of these diagrams, one for each face type, can be used to represent any stellation of the polyhedron, by shading the regions which should appear in that stellation.
A stellation diagram exists for every face of a given polyhedron. In face transitive polyhedra, symmetry can be used to require all faces have the same diagram shading. Semiregular polyhedra like the Archimedean solids will have different stellation diagrams for different kinds of faces.
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In geometry, a stellationdiagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other...
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions...
"final" because it includes all of the cells in the icosahedron's stellationdiagram. That is, every three intersecting face planes of the icosahedral...
facetings of the original hull. It is dual to the dual polyhedron's stellationdiagram, which shows all the possible edges and vertices for some face plane...
first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of...
golden ratio. The icosahedron has a large number of stellations. Coxeter et al. (1938) stated 59 stellations were identified for the regular icosahedron. The...
five regular polyhedral compounds. This compound polyhedron is also a stellation of the regular icosahedron. It was first described by Edmund Hess in 1876...
In geometry, a rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry...
represents the Ef1g1 stellation of the icosahedron. It appears in Magnus Wenninger's book Polyhedron Models as model 28, the third stellation of icosahedron...
icosahedron" ("Uniform polyhedron") at MathWorld. Weisstein, Eric W. "Fifteen stellations of the icosahedron". MathWorld. Uniform polyhedra and duals...
dual uniform polyhedra. The exterior surface also represents the De2f2 stellation of the icosahedron. These figures can be differentiated by marking which...
one of the five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund Hess in 1876. It is unique among the...
In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound. It can be seen as the compound of an icosahedron and dodecahedron...
disconnected plane figures as still being faces) coincides with one of the stellations of the icosahedron. If instead, after removing the surrounded parts of...
regular polyhedral compounds. This polyhedron can be seen as either a stellation of the icosahedron or a compound. This compound was first described by...
{5/2, 3}, having three regular star pentagonal faces around each vertex. Stellation is the process of extending the faces or edges of a polyhedron until they...
speaking {n/m} = {n/(n − m)}) and m and n are coprime (as such, all stellations of a polygon with a prime number of sides will be regular stars). Symbols...
and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a compound. The 14 Cartesian coordinates of the vertices of the compound...
meet to form a new polyhedron. Several such stellations have been described by Dorman Luke. The first stellation, often simply called the stellated rhombic...
{8/3} octagrams. Even though the stellated truncated hexahedron is a stellation of the truncated hexahedron, its core is a regular octahedron. It shares...
regular dodecahedron, as well as being a stellation of a (smaller) dodecahedron. It is the only dodecahedral stellation with this property, apart from the dodecahedron...
There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120...
dodecahedron's pentagons. Its dual, the medial triambic icosahedron, is a stellation of the icosahedron. It is topologically equivalent to a quotient space...
fully supported stellations. Another stellation of the Rhombic triacontahedron is the compound of five cubes. The total number of stellations of the rhombic...
forms a degenerate uniform compound figure. It is the second of four stellations of the dodecahedron (including the original dodecahedron itself). The...
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