by wendy » Sat Apr 07, 2018 6:09 am
The names represent the crosses and dots on the Coxeter-Dynkin diagrams.
In essence, the name consists of how many unmarked nodes appear in front, and the pattern of the marked noded.
If there is only one marked node, like o--o--x--o--o-4-o, you start at the end with the fewest o's, here the left. Count 1,2,x, gives bi- (twice) and the pattern 'x' is 'rectified. This is a bi-rectified hexaract (6-cube).
If there are several unmarked nodes, like o--o--x--o--o-4-x the pattern is still the same, but the count is different. Now you count 2,3,x from the left, and x from the right. You would still use the greek prefix as above, here (L= tri- ) and (R= none).
The next step is to convert the pattern xoox. The first x is always there, and the next positions go truncated, rhombi- and prismato- in Bowers system. The order is from right to left, so xoox is a prismato-.
A pattern of o's and x' lie oooxoxxoooo, would number 2,3,4,x from the left and 2,3,4,5,x from the right. So you use the left form, ie TETRA. The middle pattern is xoxx. which gives xorp, becomes RHOMBO-PRISMATIC. So this is a tetra-rhombo-prismatic (whatever the numbers spell).
Coxeter used Stott's system, which is to give a prefix t_a,b,c added to the base figure. The node count starts from 0, so 0o 1o 2o 3x 4o 5x 6x 7o 8o .. becomes a 'three-five-six-truncated ....