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 infinite regions are excluded from the diagram, along with any infinite portions of the lines. 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.
Other articles related to "stellations, stellation, stellation diagram":
... This follows the order in which the stellations are depicted in the book ... Where a stellation has all cells present within an outer shell, the outer shell is capitalised and the inner omitted, for example a + b + c + e1 is written as Ce1 ... Faces All of the stellations can be specified by a stellation diagram ...
Famous quotes containing the word diagram:
“Gods fire upon the wane,
A diagram hung there instead,
More women born than men.”
—William Butler Yeats (18651939)