Acronym scadaspix
Name small cellated dodecateron atop small prismated hexateron,
scad-first cap of scal
Circumradius sqrt(10/7) = 1.195229
Lace city
in approx. ASCII-art
 p   s   q		-- x3o3o3o3x (scad)
          
r   S   s 		-- o3x3o3o3x (spix)

where:
p = x3o3o3o (pen)
q = o3o3o3x (dual pen)
r = o3x3o3o (rap)
S = o3x3o3x (inv srip)
s = x3o3o3x (spid)
Confer
uniform relative:
scal  
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

xo3ox3oo3oo3xx&#x   → height = sqrt(7/12) = 0.763763
(scad || spix)

o.3o.3o.3o.3o.    | 30  * |  4  4   4   0  0 |  6 12  6  4   6  12  0   0   0  0 |  4 12 12  4  6 12   4  12  12  0  0  0  0  0  0 | 1  4  6  4 1  4 12 12  1  4  6  4 0  0  0 0 | 1 1  4  6  4 1 0
.o3.o3.o3.o3.o    |  * 60 |  0  0   2   6  3 |  0  0  0  1   6   6  3   6  12  3 |  0  0  0  0  3  3   6  12   6  3  6  2  6  6  1 | 0  0  0  0 0  3  6  3  2  6  6  2 1  3  3 2 | 0 1  3  3  1 2 1
------------------+-------+------------------+-----------------------------------+-------------------------------------------------+---------------------------------------------+-----------------
x. .. .. .. ..    |  2  0 | 60  *   *   *  * |  3  3  0  1   0   0  0   0   0  0 |  3  6  3  0  3  3   0   0   0  0  0  0  0  0  0 | 1  3  3  1 0  3  6  3  0  0  0  0 0  0  0 0 | 1 1  3  3  1 0 0
.. .. .. .. x.    |  2  0 |  * 60   *   *  * |  0  3  3  0   0   3  0   0   0  0 |  0  3  6  3  0  3   0   3   6  0  0  0  0  0  0 | 0  1  3  3 1  0  3  6  0  1  3  3 0  0  0 0 | 1 0  1  3  3 1 0
oo3oo3oo3oo3oo&#x |  1  1 |  *  * 120   *  * |  0  0  0  1   3   3  0   0   0  0 |  0  0  0  0  3  3   3   6   3  0  0  0  0  0  0 | 0  0  0  0 0  3  6  3  1  3  3  1 0  0  0 0 | 0 1  3  3  1 1 0
.. .x .. .. ..    |  0  2 |  *  *   * 180  * |  0  0  0  0   1   0  1   2   2  0 |  0  0  0  0  1  0   2   2   0  2  2  1  2  1  0 | 0  0  0  0 0  2  2  0  1  2  1  0 1  2  1 1 | 0 1  2  1  0 1 1
.. .. .. .. .x    |  0  2 |  *  *   *   * 90 |  0  0  0  0   0   2  0   0   4  2 |  0  0  0  0  0  1   0   4   4  0  2  0  2  4  1 | 0  0  0  0 0  0  2  2  0  2  4  2 0  1  2 2 | 0 0  1  2  1 2 1
------------------+-------+------------------+-----------------------------------+-------------------------------------------------+---------------------------------------------+-----------------
x.3o. .. .. ..    |  3  0 |  3  0   0   0  0 | 60  *  *  *   *   *  *   *   *  * |  2  2  0  0  1  0   0   0   0  0  0  0  0  0  0 | 1  2  1  0 0  2  2  0  0  0  0  0 0  0  0 0 | 1 1  2  1  0 0 0
x. .. .. .. x.    |  4  0 |  2  2   0   0  0 |  * 90  *  *   *   *  *   *   *  * |  0  2  2  0  0  1   0   0   0  0  0  0  0  0  0 | 0  1  2  1 0  0  2  2  0  0  0  0 0  0  0 0 | 1 0  1  2  1 0 0
.. .. .. o.3x.    |  3  0 |  0  3   0   0  0 |  *  * 60  *   *   *  *   *   *  * |  0  0  2  2  0  0   0   0   2  0  0  0  0  0  0 | 0  0  1  2 1  0  0  2  0  0  1  2 0  0  0 0 | 1 0  0  1  2 1 0
xo .. .. .. ..&#x |  2  1 |  1  0   2   0  0 |  *  *  * 60   *   *  *   *   *  * |  0  0  0  0  3  3   0   0   0  0  0  0  0  0  0 | 0  0  0  0 0  3  6  3  0  0  0  0 0  0  0 0 | 0 1  3  3  1 0 0
.. ox .. .. ..&#x |  1  2 |  0  0   2   1  0 |  *  *  *  * 180   *  *   *   *  * |  0  0  0  0  1  0   2   2   0  0  0  0  0  0  0 | 0  0  0  0 0  2  2  0  1  2  1  0 0  0  0 0 | 0 1  2  1  0 1 0
.. .. .. .. xx&#x |  2  2 |  0  1   2   0  1 |  *  *  *  *   * 180  *   *   *  * |  0  0  0  0  0  1   0   2   2  0  0  0  0  0  0 | 0  0  0  0 0  0  2  2  0  1  2  1 0  0  0 0 | 0 0  1  2  1 1 0
.o3.x .. .. ..    |  0  3 |  0  0   0   3  0 |  *  *  *  *   *   * 60   *   *  * |  0  0  0  0  1  0   0   0   0  2  2  0  0  0  0 | 0  0  0  0 0  2  2  0  0  0  0  0 1  2  1 0 | 0 1  2  1  0 0 1
.. .x3.o .. ..    |  0  3 |  0  0   0   3  0 |  *  *  *  *   *   *  * 120   *  * |  0  0  0  0  0  0   1   0   0  1  0  1  1  0  0 | 0  0  0  0 0  1  0  0  1  1  0  0 1  1  0 1 | 0 1  1  0  0 1 1
.. .x .. .. .x    |  0  4 |  0  0   0   2  2 |  *  *  *  *   *   *  *   * 180  * |  0  0  0  0  0  0   0   1   0  0  1  0  1  1  0 | 0  0  0  0 0  0  1  0  0  1  1  0 0  1  1 1 | 0 0  1  1  0 1 1
.. .. .. .o3.x    |  0  3 |  0  0   0   0  3 |  *  *  *  *   *   *  *   *   * 60 |  0  0  0  0  0  0   0   0   2  0  0  0  0  2  1 | 0  0  0  0 0  0  0  1  0  0  2  2 0  0  1 2 | 0 0  0  1  1 2 1
------------------+-------+------------------+-----------------------------------+-------------------------------------------------+---------------------------------------------+-----------------
x.3o.3o. .. ..      4  0 |  6  0   0   0  0 |  4  0  0  0   0   0  0   0   0  0 | 30  *  *  *  *  *   *   *   *  *  *  *  *  *  * | 1  1  0  0 0  1  0  0  0  0  0  0 0  0  0 0 | 1 1  1  0  0 0 0
x.3o. .. .. x.      6  0 |  6  3   0   0  0 |  2  3  0  0   0   0  0   0   0  0 |  * 60  *  *  *  *   *   *   *  *  *  *  *  *  * | 0  1  1  0 0  0  1  0  0  0  0  0 0  0  0 0 | 1 0  1  1  0 0 0
x. .. .. o.3x.      6  0 |  3  6   0   0  0 |  0  3  2  0   0   0  0   0   0  0 |  *  * 60  *  *  *   *   *   *  *  *  *  *  *  * | 0  0  1  1 0  0  0  1  0  0  0  0 0  0  0 0 | 1 0  0  1  1 0 0
.. .. o.3o.3x.      4  0 |  0  6   0   0  0 |  0  0  4  0   0   0  0   0   0  0 |  *  *  * 30  *  *   *   *   *  *  *  *  *  *  * | 0  0  0  1 1  0  0  0  0  0  0  1 0  0  0 0 | 1 0  0  0  1 1 0
xo3ox .. .. ..&#x   3  3 |  3  0   6   3  0 |  1  0  0  3   3   0  1   0   0  0 |  *  *  *  * 60  *   *   *   *  *  *  *  *  *  * | 0  0  0  0 0  2  2  0  0  0  0  0 0  0  0 0 | 0 1  2  1  0 0 0
xo .. .. .. xx&#x   4  2 |  2  2   4   0  1 |  0  1  0  2   0   2  0   0   0  0 |  *  *  *  *  * 90   *   *   *  *  *  *  *  *  * | 0  0  0  0 0  0  2  2  0  0  0  0 0  0  0 0 | 0 0  1  2  1 0 0
.. ox3oo .. ..&#x   1  3 |  0  0   3   3  0 |  0  0  0  0   3   0  0   1   0  0 |  *  *  *  *  *  * 120   *   *  *  *  *  *  *  * | 0  0  0  0 0  1  0  0  1  1  0  0 0  0  0 0 | 0 1  1  0  0 1 0
.. ox .. .. xx&#x   2  4 |  0  1   4   2  2 |  0  0  0  0   2   2  0   0   1  0 |  *  *  *  *  *  *   * 180   *  *  *  *  *  *  * | 0  0  0  0 0  0  1  0  0  1  1  0 0  0  0 0 | 0 0  1  1  0 1 0
.. .. .. oo3xx&#x   3  3 |  0  3   3   0  3 |  0  0  1  0   0   3  0   0   0  1 |  *  *  *  *  *  *   *   * 120  *  *  *  *  *  * | 0  0  0  0 0  0  0  1  0  0  1  1 0  0  0 0 | 0 0  0  1  1 1 0
.o3.x3.o .. ..      0  6 |  0  0   0  12  0 |  0  0  0  0   0   0  4   4   0  0 |  *  *  *  *  *  *   *   *   * 30  *  *  *  *  * | 0  0  0  0 0  1  0  0  0  0  0  0 1  1  0 0 | 0 1  1  0  0 0 1
.o3.x .. .. .x      0  6 |  0  0   0   6  3 |  0  0  0  0   0   0  2   0   3  0 |  *  *  *  *  *  *   *   *   *  * 60  *  *  *  * | 0  0  0  0 0  0  1  0  0  0  0  0 0  1  1 0 | 0 0  1  1  0 0 1
.. .x3.o3.o ..      0  4 |  0  0   0   6  0 |  0  0  0  0   0   0  0   4   0  0 |  *  *  *  *  *  *   *   *   *  *  * 30  *  *  * | 0  0  0  0 0  0  0  0  1  0  0  0 1  0  0 1 | 0 1  0  0  0 1 1
.. .x3.o .. .x      0  6 |  0  0   0   6  3 |  0  0  0  0   0   0  0   2   3  0 |  *  *  *  *  *  *   *   *   *  *  *  * 60  *  * | 0  0  0  0 0  0  0  0  0  1  0  0 0  1  0 1 | 0 0  1  0  0 1 1
.. .x .. .o3.x      0  6 |  0  0   0   3  6 |  0  0  0  0   0   0  0   0   3  2 |  *  *  *  *  *  *   *   *   *  *  *  *  * 60  * | 0  0  0  0 0  0  0  0  0  0  1  0 0  0  1 1 | 0 0  0  1  0 1 1
.. .. .o3.o3.x      0  4 |  0  0   0   0  6 |  0  0  0  0   0   0  0   0   0  4 |  *  *  *  *  *  *   *   *   *  *  *  *  *  * 15 | 0  0  0  0 0  0  0  0  0  0  0  2 0  0  0 2 | 0 0  0  0  1 2 1
------------------+-------+------------------+-----------------------------------+-------------------------------------------------+---------------------------------------------+-----------------
x.3o.3o.3o. ..      5  0 | 10  0   0   0  0 | 10  0  0  0   0   0  0   0   0  0 |  5  0  0  0  0  0   0   0   0  0  0  0  0  0  0 | 6  *  *  * *  *  *  *  *  *  *  * *  *  * * | 1 1  0  0  0 0 0
x.3o.3o. .. x.      8  0 | 12  4   0   0  0 |  8  6  0  0   0   0  0   0   0  0 |  2  4  0  0  0  0   0   0   0  0  0  0  0  0  0 | * 15  *  * *  *  *  *  *  *  *  * *  *  * * | 1 0  1  0  0 0 0
x.3o. .. o.3x.      9  0 |  9  9   0   0  0 |  3  9  3  0   0   0  0   0   0  0 |  0  3  3  0  0  0   0   0   0  0  0  0  0  0  0 | *  * 20  * *  *  *  *  *  *  *  * *  *  * * | 1 0  0  1  0 0 0
x. .. o.3o.3x.      8  0 |  4 12   0   0  0 |  0  6  8  0   0   0  0   0   0  0 |  0  0  4  2  0  0   0   0   0  0  0  0  0  0  0 | *  *  * 15 *  *  *  *  *  *  *  * *  *  * * | 1 0  0  0  1 0 0
.. o.3o.3o.3x.      5  0 |  0 10   0   0  0 |  0  0 10  0   0   0  0   0   0  0 |  0  0  0  5  0  0   0   0   0  0  0  0  0  0  0 | *  *  *  * 6  *  *  *  *  *  *  * *  *  * * | 1 0  0  0  0 1 0
xo3ox3oo .. ..&#x   4  6 |  6  0  12  12  0 |  4  0  0  6  12   0  4   4   0  0 |  1  0  0  0  4  0   4   0   0  1  0  0  0  0  0 | *  *  *  * * 30  *  *  *  *  *  * *  *  * * | 0 1  1  0  0 0 0
xo3ox .. .. xx&#x   6  6 |  6  3  12   6  3 |  2  3  0  6   6   6  2   0   3  0 |  0  1  0  0  2  3   0   3   0  0  1  0  0  0  0 | *  *  *  * *  * 60  *  *  *  *  * *  *  * * | 0 0  1  1  0 0 0
xo .. .. oo3xx&#x   6  3 |  3  6   6   0  3 |  0  3  2  3   0   6  0   0   0  1 |  0  0  1  0  0  3   0   0   2  0  0  0  0  0  0 | *  *  *  * *  *  * 60  *  *  *  * *  *  * * | 0 0  0  1  1 0 0
.. ox3oo3oo ..&#x   1  4 |  0  0   4   6  0 |  0  0  0  0   6   0  0   4   0  0 |  0  0  0  0  0  0   4   0   0  0  0  1  0  0  0 | *  *  *  * *  *  *  * 30  *  *  * *  *  * * | 0 1  0  0  0 1 0
.. ox3oo .. xx&#x   2  6 |  0  1   6   6  3 |  0  0  0  0   6   3  0   2   3  0 |  0  0  0  0  0  0   2   3   0  0  0  0  1  0  0 | *  *  *  * *  *  *  *  * 60  *  * *  *  * * | 0 0  1  0  0 1 0
.. ox .. oo3xx&#x   3  6 |  0  3   6   3  6 |  0  0  1  0   3   6  0   0   3  2 |  0  0  0  0  0  0   0   3   2  0  0  0  0  1  0 | *  *  *  * *  *  *  *  *  * 60  * *  *  * * | 0 0  0  1  0 1 0
.. .. oo3oo3xx&#x   4  4 |  0  6   4   0  6 |  0  0  4  0   0   6  0   0   0  4 |  0  0  0  1  0  0   0   0   4  0  0  0  0  0  1 | *  *  *  * *  *  *  *  *  *  * 30 *  *  * * | 0 0  0  0  1 1 0
.o3.x3.o3.o ..      0 10 |  0  0   0  30  0 |  0  0  0  0   0   0 10  20   0  0 |  0  0  0  0  0  0   0   0   0  5  0  5  0  0  0 | *  *  *  * *  *  *  *  *  *  *  * 6  *  * * | 0 1  0  0  0 0 1
.o3.x3.o .. .x      0 12 |  0  0   0  24  6 |  0  0  0  0   0   0  8   8  12  0 |  0  0  0  0  0  0   0   0   0  2  4  0  4  0  0 | *  *  *  * *  *  *  *  *  *  *  * * 15  * * | 0 0  1  0  0 0 1
.o3.x .. .o3.x      0  9 |  0  0   0   9  9 |  0  0  0  0   0   0  3   0   9  3 |  0  0  0  0  0  0   0   0   0  0  3  0  0  3  0 | *  *  *  * *  *  *  *  *  *  *  * *  * 20 * | 0 0  0  1  0 0 1
.. .x3.o3.o3.x      0 20 |  0  0   0  30 30 |  0  0  0  0   0   0  0  20  30 20 |  0  0  0  0  0  0   0   0   0  0  0  5 10 10  5 | *  *  *  * *  *  *  *  *  *  *  * *  *  * 6 | 0 0  0  0  0 1 1
------------------+-------+------------------+-----------------------------------+-------------------------------------------------+---------------------------------------------+-----------------
x.3o.3o.3o.3x.     30  0 | 60 60   0   0  0 | 60 90 60  0   0   0  0   0   0  0 | 30 60 60 30  0  0   0   0   0  0  0  0  0  0  0 | 6 15 20 15 6  0  0  0  0  0  0  0 0  0  0 0 | 1 *  *  *  * * *
xo3ox3oo3oo ..&#x   5 10 | 10  0  20  30  0 | 10  0  0 10  30   0 10  20   0  0 |  5  0  0  0 10  0  20   0   0  5  0  5  0  0  0 | 1  0  0  0 0  5  0  0  5  0  0  0 1  0  0 0 | * 6  *  *  * * *
xo3ox3oo .. xx&#x   8 12 | 12  4  24  24  6 |  8  6  0 12  24  12  8   8  12  0 |  2  4  0  0  8  6   8  12   0  2  4  0  4  0  0 | 0  1  0  0 0  2  4  0  0  4  0  0 0  1  0 0 | * * 15  *  * * *
xo3ox .. oo3xx&#x   9  9 |  9  9  18   9  9 |  3  9  3  9   9  18  3   0   9  3 |  0  3  3  0  3  9   0   9   6  0  3  0  0  3  0 | 0  0  1  0 0  0  3  3  0  0  3  0 0  0  1 0 | * *  * 20  * * *
xo .. oo3oo3xx&#x   8  4 |  4 12   8   0  6 |  0  6  8  4   0  12  0   0   0  4 |  0  0  4  2  0  6   0   0   8  0  0  0  0  0  1 | 0  0  0  1 0  0  0  4  0  0  0  2 0  0  0 0 | * *  *  * 15 * *
.. ox3oo3oo3xx&#x   5 20 |  0 10  20  30 30 |  0  0 10  0  30  30  0  20  30 20 |  0  0  0  5  0  0  20  30  20  0  0  5 10 10  5 | 0  0  0  0 1  0  0  0  5 10 10  5 0  0  0 1 | * *  *  *  * 6 *
.o3.x3.o3.o3.x      0 60 |  0  0   0 180 90 |  0  0  0  0   0   0 60 120 180 60 |  0  0  0  0  0  0   0   0   0 30 60 30 60 60 15 | 0  0  0  0 0  0  0  0  0  0  0  0 6 15 20 6 | * *  *  *  * * 1

© 2004-2021
top of page