Brick symmetry (InstanceAttribute, 4)

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Revision as of 21:10, 3 March 2014

Brick symmetry is a family of n-dimensional symmetry groups of order 2ⁿ, where the existence of any point (x, y, z, ...) in the figure implies the existence of all the points (±x, ±y, ±z, ...). If a figure has brick symmetry, it is said to be a brick. The importance of bricks and brick symmetry stems from the requirement that powertope exponents must be bricks.

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 <[#ontology [kind class] [cats Shape]]>
+'''Brick symmetry''' is a family of ''n''-dimensional [[symmetry group]]s of order 2<sup>''n''</sup>, where the existence of any point (''x'', ''y'', ''z'', ...) in the figure implies the existence of all the points (±''x'', ±''y'', ±''z'', ...). If a figure has brick symmetry, it is said to be a ''brick''. The importance of bricks and brick symmetry stems from the requirement that [[powertope]] exponents must be bricks.
-A '''brick''' is a [[shape]] with ''brick symmetry''. A shape has brick symmetry [[wikipedia:If and only if|iff]] the fact that it contains a point (x, y, z, ...) implies that it contains all the points (±x, ±y, ±z, ...).
-The set of bricks is equivalent to the set of shapes that can be used as [[powertope]] exponents.