In geometry, an infinite skew polyhedron is an extension of the idea of a polyhedron, consisting of regular polygon faces with nonplanar vertex figures, allowing the figure to extend indefinitely without folding round to form a closed surface.
Infinite skew polyhedra have also been called polyhedral sponges, and also hyperbolic tessellations because they can be seen as related to hyperbolic space tessellations which also have negative angle defects. They are examples of the more general class of infinite polyhedra, or apeirohedra.
Many are directly related to a convex uniform honeycomb, being the polygonal surface of a honeycomb with some of the cells removed. Characteristically, an infinite skew polyhedron divides space into two halves. If one half is thought of as solid the figure is sometimes called a partial honeycomb.
Read more about Infinite Skew Polyhedron: Regular Skew Polyhedra, Gott's Regular Pseudopolyhedrons, Semiregular Infinite Skew Polyhedra
Famous quotes containing the word infinite:
“Nothing could his enemies do but it rebounded to his infinite advantage,—that is, to the advantage of his cause.... No theatrical manager could have arranged things so wisely to give effect to his behavior and words. And who, think you, was the manager? Who placed the slave-woman and her child, whom he stooped to kiss for a symbol, between his prison and the gallows?”
—Henry David Thoreau (1817–1862)