r     R   		-- o3o3x3o3o (dot)
             
P     S     p		-- x3o3o3o3x (scad)

where:
r = o3x3o3o (rap)
R = o3o3x3o (inv. rap)
p = x3o3o3o (pen)
P = o3o3o3x (dual pen)
S = x3o3o3x (spid)

o   A   V   o	-- o3o3x3o3o (dot)
             
  V   +   A  	-- x3o3o3o3x (scad)

where:
o =  o3o   o3o      (point)
A =  x3o   x3o      (triddip)
V =  o3x   o3x      (bi-inv. triddip)
+ = xo3xo ox3ox&#zq (bihexagonal tegum)

a     O     b		-- o3o3x3o3o (dot)
             
B     c     A		-- x3o3o3o3x (scad)

where:
a = x3o3o o (tet)
b = o3o3x o (dual tet)
A = x3o3o x (tepe)
B = o3o3x x (inv. tepe)
O = o3x3o x (ope)
c = compound of
    x3o3x o (co)
    o3o3o u (ortho u-line)

Incidence matrix according to Dynkin symbol

ox3oo3xo3oo3ox&#x   → height = 1/2
(dot || scad)

o.3o.3o.3o.3o.      | 20  * |  9   9   0 |  18  18  36   0  0 |  6  9   6  36   9  36  0   0 |  6 12   6  18  9  9  0  0  0 | 1  6  6  1 0
.o3.o3.o3.o3.o      |  * 30 |  0   6   8 |   0  24  12  12 12 |  0  0  12  24  24   8  8  24 |  0  8  24   8 12  1  2  8  6 | 0  2  8  6 1
--------------------+-------+------------+--------------------+------------------------------+------------------------------+-------------
.. .. x. .. ..      |  2  0 | 90   *   * |   4   0   4   0  0 |  2  4   0   4   0   8  0   0 |  4  4   0   4  1  4  0  0  0 | 1  4  2  0 0
oo3oo3oo3oo3oo&#x   |  1  1 |  * 180   * |   0   4   4   0  0 |  0  0   2   8   4   4  0   0 |  0  4   4   4  4  1  0  0  0 | 0  2  4  1 0
.x .. .. .. ..    & |  0  2 |  *   * 120 |   0   3   0   3  3 |  0  0   3   3   6   0  3   9 |  0  3   9   1  3  0  1  4  3 | 0  1  4  3 1
--------------------+-------+------------+--------------------+------------------------------+------------------------------+-------------
.. o.3x. .. ..    & |  3  0 |  3   0   0 | 120   *   *   *  * |  1  2   0   0   0   2  0   0 |  3  2   0   1  0  2  0  0  0 | 1  3  1  0 0
ox .. .. .. ..&#x & |  1  2 |  0   2   1 |   * 360   *   *  * |  0  0   1   2   2   0  0   0 |  0  2   3   1  2  0  0  0  0 | 0  1  3  1 0
.. .. xo .. ..&#x   |  2  1 |  1   2   0 |   *   * 360   *  * |  0  0   0   2   0   2  0   0 |  0  2   0   2  1  1  0  0  0 | 0  2  2  0 0
.x3.o .. .. ..    & |  0  3 |  0   0   3 |   *   *   * 120  * |  0  0   1   0   0   0  2   2 |  0  2   2   0  0  0  1  2  1 | 0  1  2  1 1
.x .. .. .. .x      |  0  4 |  0   0   4 |   *   *   *   * 90 |  0  0   0   0   2   0  0   4 |  0  0   4   0  1  0  0  2  2 | 0  0  2  2 1
--------------------+-------+------------+--------------------+------------------------------+------------------------------+-------------
o.3o.3x. .. ..    & ♦  4  0 |  6   0   0 |   4   0   0   0  0 | 30  *   *   *   *   *  *   * |  2  2   0   0  0  0  0  0  0 | 1  2  1  0 0
.. o.3x.3o. ..      ♦  6  0 | 12   0   0 |   8   0   0   0  0 |  * 30   *   *   *   *  *   * |  2  0   0   0  0  1  0  0  0 | 1  2  0  0 0
ox3oo .. .. ..&#x & ♦  1  3 |  0   3   3 |   0   3   0   1  0 |  *  * 120   *   *   *  *   * |  0  2   2   0  0  0  0  0  0 | 0  1  2  1 0
ox .. xo .. ..&#x & ♦  2  2 |  1   4   1 |   0   2   2   0  0 |  *  *   * 360   *   *  *   * |  0  1   0   1  1  0  0  0  0 | 0  1  2  0 0
ox .. .. .. ox&#x   ♦  1  4 |  0   4   4 |   0   4   0   0  1 |  *  *   *   * 180   *  *   * |  0  0   2   0  1  0  0  0  0 | 0  0  2  1 0
.. oo3xo .. ..&#x & ♦  3  1 |  3   3   0 |   1   0   3   0  0 |  *  *   *   *   * 240  *   * |  0  1   0   1  0  1  0  0  0 | 0  2  1  0 0
.x3.o3.o .. ..    & ♦  0  4 |  0   0   6 |   0   0   0   4  0 |  *  *   *   *   *   * 60   * |  0  1   0   0  0  0  1  1  0 | 0  1  1  0 1
.x3.o .. .. .x    & ♦  0  6 |  0   0   9 |   0   0   0   2  3 |  *  *   *   *   *   *  * 120 |  0  0   1   0  0  0  0  1  1 | 0  0  1  1 1
--------------------+-------+------------+--------------------+------------------------------+------------------------------+-------------
o.3o.3x.3o. ..    & ♦ 10  0 | 30   0   0 |  30   0   0   0  0 |  5  5   0   0   0   0  0   0 | 12  *   *   *  *  *  *  *  * | 1  1  0  0 0
ox3oo3xo .. ..&#x & ♦  4  4 |  6  12   6 |   4  12  12   4  0 |  1  0   4   6   0   4  1   0 |  * 60   *   *  *  *  *  *  * | 0  1  1  0 0
ox3oo .. .. ox&#x & ♦  1  6 |  0   6   9 |   0   9   0   2  3 |  0  0   2   0   3   0  0   1 |  *  * 120   *  *  *  *  *  * | 0  0  1  1 0
ox .. xo3oo ..&#x & ♦  3  2 |  3   6   1 |   1   3   6   0  0 |  0  0   0   3   0   2  0   0 |  *  *   * 120  *  *  *  *  * | 0  1  1  0 0
ox .. xo .. ox&#x   ♦  2  4 |  1   8   4 |   0   8   4   0  1 |  0  0   0   4   2   0  0   0 |  *  *   *   * 90  *  *  *  * | 0  0  2  0 0
.. oo3xo3oo ..&#x   ♦  6  1 | 12   6   0 |   8   0  12   0  0 |  0  1   0   0   0   8  0   0 |  *  *   *   *  * 30  *  *  * | 0  2  0  0 0
.x3.o3.o3.o ..    & ♦  0  5 |  0   0  10 |   0   0   0  10  0 |  0  0   0   0   0   0  5   0 |  *  *   *   *  *  * 12  *  * | 0  1  0  0 1
.x3.o3.o .. .x    & ♦  0  8 |  0   0  16 |   0   0   0   8  6 |  0  0   0   0   0   0  2   4 |  *  *   *   *  *  *  * 30  * | 0  0  1  0 1
.x3.o .. .o3.x      ♦  0  9 |  0   0  18 |   0   0   0   6  9 |  0  0   0   0   0   0  0   6 |  *  *   *   *  *  *  *  * 20 | 0  0  0  1 1
--------------------+-------+------------+--------------------+------------------------------+------------------------------+-------------
o.3o.3x.3o.3o.      ♦ 20  0 | 90   0   0 | 120   0   0   0  0 | 30 30   0   0   0   0  0   0 | 12  0   0   0  0  0  0  0  0 | 1  *  *  * *
ox3oo3xo3oo ..&#x & ♦ 10  5 | 30  30  10 |  30  30  60  10  0 |  5  5  10  30   0  40  5   0 |  1  5   0  10  0  5  1  0  0 | * 12  *  * *
ox3oo3xo .. ox&#x & ♦  4  8 |  6  24  16 |   4  36  24   8  6 |  1  0   8  24  12   8  2   4 |  0  2   4   4  6  0  0  1  0 | *  * 30  * *
ox3oo .. oo3ox&#x   ♦  1  9 |  0   9  18 |   0  18   0   6  9 |  0  0   6   0   9   0  0   6 |  0  0   6   0  0  0  0  0  1 | *  *  * 20 *
.x3.o3.o3.o3.x      ♦  0 30 |  0   0 120 |   0   0   0 120 90 |  0  0   0   0   0   0 60 120 |  0  0   0   0  0  0 12 30 20 | *  *  *  * 1