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Skew apeirohedron information


In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend indefinitely without folding round to form a closed surface.

Skew apeirohedra have also been called polyhedral sponges.

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 3-dimensional space into two halves. If one half is thought of as solid the figure is sometimes called a partial honeycomb.

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Skew apeirohedron

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In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend...

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Regular skew apeirohedron

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In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron. They have either skew regular faces or skew regular vertex figures. In...

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Skew polygon

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Petrie polygon Quadrilateral § Skew quadrilaterals Regular skew polyhedron Skew apeirohedron (infinite skew polyhedron) Skew lines Coxeter 1973, §1.1 Regular...

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Cubic honeycomb

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specify how many cells exist around the edge. It is related to a skew apeirohedron with vertex configuration 4.4.6.6, with the octagons and some of the...

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List of regular polytopes

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2-apeirotope or apeirogon is an infinite polygon, a 3-apeirotope or apeirohedron is an infinite polyhedron, etc. There are two main geometric classes...

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Toroidal polyhedron

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self-intersecting and topologically self-dual. Projective polyhedron Skew apeirohedron (infinite skew polyhedron) Spherical polyhedron Toroidal graph Whiteley (1979);...

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List of mathematical shapes

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honeycomb Tesseractic honeycomb honeycomb Apeirotope Apeirogon Apeirohedron Regular skew polyhedron Abstract polytope 11-cell 57-cell Convex polygon Concave...

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Bitruncated cubic honeycomb

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The regular skew apeirohedron {6,4|4} contains the hexagons of this honeycomb....

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Quarter cubic honeycomb

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The subset of hexagonal faces of this honeycomb contains a regular skew apeirohedron {6,6|3}. Four sets of parallel planes of trihexagonal tilings exist...

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Complex polytope

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leaving ordinary 2-edges. Three of them are related to the finite regular skew polyhedron in R 4 {\displaystyle \mathbb {R} ^{4}} . Coxeter defines other...

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