Wythoff Symbol - Summary Table

Summary Table

There are seven generator points with each set of p,q,r (and a few special forms):

General				Right triangle (r=2)
Description	Wythoff symbol	Vertex configuration	Coxeter diagram	Wythoff symbol	Vertex configuration	Schläfli symbol	Coxeter diagram
regular and quasiregular	q \| p r	(p.r)q		q \| p 2	pq	{p,q}
	p \| q r	(q.r)p		p \| q 2	qp	{q,p}
	r \| p q	(q.p)r		2 \| p q	(q.p)²	t₁{p,q}
truncated and expanded	q r \| p	q.2p.r.2p		q 2 \| p	q.2p.2p	t_0,1{p,q}
	p r \| q	p.2q.r.2q		p 2 \| q	p. 2q.2q	t_0,1{q,p}
	p q \| r	2r.q.2r.p		p q \| 2	4.q.4.p	t_0,2{p,q}
even-faced	p q r \|	2r.2q.2p		p q 2 \|	4.2q.2p	t_0,1,2{p,q}
even-faced	p q (r s) \|	2p.2q.-2p.-2q	-	p 2 (r s) \|	2p.4.-2p.4/₃		-
snub	\| p q r	3.r.3.q.3.p		\| p q 2	3.3.q.3.p	s{p,q}
snub	\| p q r s	(4.p.4.q.4.r.4.s)/2	-	-	-		-

There are three special cases:

p q (r s) | – This is a mixture of p q r | and p q s |.
| p q r – Snub forms (alternated) are give this otherwise unused symbol.
| p q r s – A unique snub form for U75 that isn't Wythoff-constructible.

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