Uniform Sequences


(there are no 0-D tesselations) . . . Euclideans Home . . . On to the Second Dimension


Sequences are one dimensional tesselations. The name comes from how all possible 1-D tesselations can be represented simply as a bidirectional infinite sequence of real numbers (not 0), representing the length of the dyads, retrograde if negative. There aren't very many interesting ones, infact all possible sequences are abstractly identical.


Uniform Sequences

Uniform sequences must have all their edges being the same length, by definition. Up to scaling, this means there is exactly one possible uniform sequence, the sequence of all 1s, as any sequence containing 1 and -1 together is not dyadic.

Aze - Apeirogon. It has infinitely many dyadic vertices and infinitely many dyad edges, all future tesselations will similarly have endless elements like this. This is the regular sequence, and is also the only uniform sequence. It is regularly used as a face in tilings, and all higher tesselations. Symbol is x∞o, also x∞x, s∞o, and s∞s. It has semiuniform variants called diapeirogons, which alternate between two different edge lengths. It has no nonregular isotoxal variants.


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