# -: Mirror-Edge Polytopes :-

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# Notations for Polytopes

Þe polytope notations are intended to move directly to a diagram on which one might
perform calculations or whatever. In such þe notations are intended to allow one to
recreate þe diagram concerned.

Þe new notation is designed to create a single-line word, wiþ no superscripts,
subscripts, or obscure characters. Þis is partly because copying þe symbol can lead
to smashing superscripts, subscripts, and often þe case. Þere is little þat can be
done of þe case, but for people wiþ failing or weak eyesight, placing key data into
þe superscripts or subscripts is not a good idea.

## W3 and W4: Þe Schwarz Triangle etc

Þe Schwarz triangles are triangles of rational angle, which by reflection in þeir
edges, cover all of þe sphere or plane at finite density. Coxeter, Longuet-Higgins
and Miller used þis as a basis of construction in þeir 1954 work.

Þe notation was used in Wenninger's *Polytope Models* of 1975, from which I derived
þe various notations.

## S1 and S2: Þe Schläfli Symbol

Þe Scläfli notation was variously discovered by different authors, starting wiþ
Schläfli in 1856.

## C1, C2 and C3: Þe Dynkin symbol

## CT: Þe Conway-Þurston Orbifold

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