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 t0,1{p,q}
p r | q p.2q.r.2q p 2 | q p. 2q.2q t0,1{q,p}
p q | r 2r.q.2r.p p q | 2 4.q.4.p t0,2{p,q}
even-faced p q r | 2r.2q.2p p q 2 | 4.2q.2p t0,1,2{p,q}
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}
| 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.

Read more about this topic:  Wythoff Symbol

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