Brick symmetry (InstanceAttribute, 4)
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| - | '''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. | + | '''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 [[brick product]] operators and [[powertope]] exponents must be bricks. |
In three dimensions, brick symmetry is known as ''biprismatic symmetry'', D<sub>2h</sub>. Its supergroups are the even [[prismatic symmetries]] D<sub>''n''h</sub> with ''n'' even, the [[staurohedral symmetry]] O<sub>h</sub>, the [[rhodohedral symmetry]] I<sub>h</sub> and the [[pyritohedral symmetry]] T<sub>h</sub>. | In three dimensions, brick symmetry is known as ''biprismatic symmetry'', D<sub>2h</sub>. Its supergroups are the even [[prismatic symmetries]] D<sub>''n''h</sub> with ''n'' even, the [[staurohedral symmetry]] O<sub>h</sub>, the [[rhodohedral symmetry]] I<sub>h</sub> and the [[pyritohedral symmetry]] T<sub>h</sub>. | ||
Revision as of 21:18, 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 brick product operators and powertope exponents must be bricks.
In three dimensions, brick symmetry is known as biprismatic symmetry, D2h. Its supergroups are the even prismatic symmetries Dnh with n even, the staurohedral symmetry Oh, the rhodohedral symmetry Ih and the pyritohedral symmetry Th.
