# Brick symmetry (InstanceAttribute, 4)

### From Hi.gher. Space

**Brick symmetry** is a family of *n*-dimensional symmetry groups of order 2^{n}, 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_{2h}. Its supergroups are the even prismatic symmetries D_{kh} with *k* even, the staurohedral symmetry O_{h}, the rhodohedral symmetry I_{h} and the pyritohedral symmetry T_{h}.