LAUSR

The dimensions 2, 8 and 24 play significant roles in lattice theory. In Clifford algebra theory there are well-known periodicities of the first two of these dimensions. Using novel representations of the purely Euclidean Clifford algebras over all four of the division algebras, $${\mathbf{R}}$$R, $${\mathbf{C}}$$C, $${\mathbf{H}}$$H, and $${\mathbf{O}}$$O, a door is opened to a Clifford algebra periodicity of order 24 as well.