A prismatic polytope is a dimensional generalization of a prism. An n-dimensional prismatic polytope is constructed from two (n − 1)-dimensional polytopes, translated into the next dimension.
The prismatic n-polytope elements are doubled from the (n − 1)-polytope elements and then creating new elements from the next lower element.
Take an n-polytope with fi i-face elements (i = 0, ..., n). Its (n + 1)-polytope prism will have 2fi + fi−1 i-face elements. (With f−1 = 0, fn = 1.)
By dimension:
- Take a polygon with n vertices, n edges. Its prism has 2n vertices, 3n edges, and 2 + n faces.
- Take a polyhedron with v vertices, e edges, and f faces. Its prism has 2v vertices, 2e + v edges, 2f + e faces, and 2 + f cells.
- Take a polychoron with v vertices, e edges, f faces and c cells. Its prism has 2v vertices, 2e + v edges, 2f + e faces, and 2c + f cells, and 2 + c hypercells.
Read more about this topic: Prism (geometry)
Famous quotes containing the word prismatic:
“Then a small rainbow like a trellis gate,
A very small moon-made prismatic bow,
Stood closely over us through which to go.”
—Robert Frost (1874–1963)