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If a geometric shape can be used as a prototile to create a tessellation, the shape is said to tessellate or to tile the plane. The Conway criterion is a sufficient, but not necessary, set of rules for deciding whether a given shape tiles the plane periodically without reflections: some tiles fail the criterion, but still tile the plane. [19]
The metals used in granulation are usually gold and/or silver alloys of high purity – alloys below 18 kt. gold and sterling silver being unsuitable. With each technique, the process begins with the making of the granules themselves. [2] The granules are made from the same material as the base to which they will be affixed.
The rhombic dodecahedron is a space-filling polyhedron, meaning it can be applied to tessellate three-dimensional space: it can be stacked to fill a space, much like hexagons fill a plane. It is a parallelohedron because it can be space-filling a honeycomb in which all of its copies meet face-to-face. [7]
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In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by recreational mathematician Solomon W. Golomb and popularized by Martin Gardner in his " Mathematical Games " column in the May 1963 issue of Scientific American . [ 1 ]
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Regular complex apeirogons have vertices and edges, where edges can contain 2 or more vertices. Regular apeirogons p{q}r are constrained by: 1/p + 2/q + 1/r = 1. Edges have p vertices, and vertex figures are r-gonal. [5] The first is made of 2-edges, three around every vertex, the second has hexagonal edges, three around every vertex.
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