Acronym scadip
Name small-cellated-dodecateric prism
Circumradius sqrt(5)/2 = 1.118034
Volume 21 sqrt(3)/40 = 0.909327
Confer
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

x x3o3o3o3x

. . . . . . | 60 |  1   4   4 |  4  4   6  12   6 |  6 12  6  4  12  12  4 |  4 12 12  4  1  4  6  4  1 | 1  4  6  4 1 1
------------+----+------------+-------------------+------------------------+----------------------------+---------------
x . . . . . |  2 | 30   *   * |  4  4   0   0   0 |  6 12  6  0   0   0  0 |  4 12 12  4  0  0  0  0  0 | 1  4  6  4 1 0
. x . . . . |  2 |  * 120   * |  1  0   3   3   0 |  3  3  0  3   6   3  0 |  3  6  3  0  1  3  3  1  0 | 1  3  3  1 0 1
. . . . . x |  2 |  *   * 120 |  0  1   0   3   3 |  0  3  3  0   3   6  3 |  0  3  6  3  0  1  3  3  1 | 0  1  3  3 1 1
------------+----+------------+-------------------+------------------------+----------------------------+---------------
x x . . . . |  4 |  2   2   0 | 60  *   *   *   * |  3  3  0  0   0   0  0 |  3  6  3  0  0  0  0  0  0 | 1  3  3  1 0 0
x . . . . x |  4 |  2   0   2 |  * 60   *   *   * |  0  3  3  0   0   0  0 |  0  3  6  3  0  0  0  0  0 | 0  1  3  3 1 0
. x3o . . . |  3 |  0   3   0 |  *  * 120   *   * |  1  0  0  2   2   0  0 |  2  2  0  0  1  2  1  0  0 | 1  2  1  0 0 1
. x . . . x |  4 |  0   2   2 |  *  *   * 180   * |  0  1  0  0   2   2  0 |  0  2  2  0  0  1  2  1  0 | 0  1  2  1 0 1
. . . . o3x |  3 |  0   0   3 |  *  *   *   * 120 |  0  0  1  0   0   2  2 |  0  0  2  2  0  0  1  2  1 | 0  0  1  2 1 1
------------+----+------------+-------------------+------------------------+----------------------------+---------------
x x3o . . .   6 |  3   6   0 |  3  0   2   0   0 | 60  *  *  *   *   *  * |  2  2  0  0  0  0  0  0  0 | 1  2  1  0 0 0
x x . . . x   8 |  4   4   4 |  2  2   0   2   0 |  * 90  *  *   *   *  * |  0  2  2  0  0  0  0  0  0 | 0  1  2  1 0 0
x . . . o3x   6 |  3   0   6 |  0  3   0   0   2 |  *  * 60  *   *   *  * |  0  0  2  2  0  0  0  0  0 | 0  0  1  2 1 0
. x3o3o . .   4 |  0   6   0 |  0  0   4   0   0 |  *  *  * 60   *   *  * |  1  0  0  0  1  1  0  0  0 | 1  1  0  0 0 1
. x3o . . x   6 |  0   6   3 |  0  0   2   3   0 |  *  *  *  * 120   *  * |  0  1  0  0  0  1  1  0  0 | 0  1  1  0 0 1
. x . . o3x   6 |  0   3   6 |  0  0   0   3   2 |  *  *  *  *   * 120  * |  0  0  1  0  0  0  1  1  0 | 0  0  1  1 0 1
. . . o3o3x   4 |  0   0   6 |  0  0   0   0   4 |  *  *  *  *   *   * 60 |  0  0  0  1  0  0  0  1  1 | 0  0  0  1 1 1
------------+----+------------+-------------------+------------------------+----------------------------+---------------
x x3o3o . .   8 |  4  12   0 |  6  0   8   0   0 |  4  0  0  2   0   0  0 | 30  *  *  *  *  *  *  *  * | 1  1  0  0 0 0
x x3o . . x  12 |  6  12   6 |  6  3   4   6   0 |  2  3  0  0   2   0  0 |  * 60  *  *  *  *  *  *  * | 0  1  1  0 0 0
x x . . o3x  12 |  6   6  12 |  3  6   0   6   4 |  0  3  2  0   0   2  0 |  *  * 60  *  *  *  *  *  * | 0  0  1  1 0 0
x . . o3o3x   8 |  4   0  12 |  0  6   0   0   8 |  0  0  4  0   0   0  2 |  *  *  * 30  *  *  *  *  * | 0  0  0  1 1 0
. x3o3o3o .   5 |  0  10   0 |  0  0  10   0   0 |  0  0  0  5   0   0  0 |  *  *  *  * 12  *  *  *  * | 1  0  0  0 0 1
. x3o3o . x   8 |  0  12   4 |  0  0   8   6   0 |  0  0  0  2   4   0  0 |  *  *  *  *  * 30  *  *  * | 0  1  0  0 0 1
. x3o . o3x   9 |  0   9   9 |  0  0   3   9   3 |  0  0  0  0   3   3  0 |  *  *  *  *  *  * 40  *  * | 0  0  1  0 0 1
. x . o3o3x   8 |  0   4  12 |  0  0   0   6   8 |  0  0  0  0   0   4  2 |  *  *  *  *  *  *  * 30  * | 0  0  0  1 0 1
. . o3o3o3x   5 |  0   0  10 |  0  0   0   0  10 |  0  0  0  0   0   0  5 |  *  *  *  *  *  *  *  * 12 | 0  0  0  0 1 1
------------+----+------------+-------------------+------------------------+----------------------------+---------------
x x3o3o3o .  10 |  5  20   0 | 10  0  20   0   0 | 10  0  0 10   0   0  0 |  5  0  0  0  2  0  0  0  0 | 6  *  *  * * *
x x3o3o . x  16 |  8  24   8 | 12  4  16  12   0 |  8  6  0  4   8   0  0 |  2  4  0  0  0  2  0  0  0 | * 15  *  * * *
x x3o . o3x  18 |  9  18  18 |  9  9   6  18   6 |  3  9  3  0   6   6  0 |  0  3  3  0  0  0  2  0  0 | *  * 20  * * *
x x . o3o3x  16 |  8   8  24 |  4 12   0  12  16 |  0  6  8  0   0   8  4 |  0  0  4  2  0  0  0  2  0 | *  *  * 15 * *
x . o3o3o3x  10 |  5   0  20 |  0 10   0   0  20 |  0  0 10  0   0   0 10 |  0  0  0  5  0  0  0  0  2 | *  *  *  * 6 *
. x3o3o3o3x  30 |  0  60  60 |  0  0  60  90  60 |  0  0  0 30  60  60 30 |  0  0  0  0  6 15 20 15  6 | *  *  *  * * 2

xx3oo3oo3oo3xx&#x   → height = 1

o.3o.3o.3o.3o.    | 30  * |  4  4  1  0  0 |  6 12  6  4  4  0  0  0 |  4 12 12  4  6 12  6  0  0  0  0 | 1  4  6  4 1  4 12 12  4 0  0  0  0 0 | 1 1  4  6  4 1 0
.o3.o3.o3.o3.o    |  * 30 |  0  0  1  4  4 |  0  0  0  4  4  6 12  6 |  0  0  0  0  6 12  6  4 12 12  4 | 0  0  0  0 0  4 12 12  4 1  4  6  4 1 | 0 1  4  6  4 1 1
------------------+-------+----------------+-------------------------+----------------------------------+---------------------------------------+-----------------
x. .. .. .. ..    |  2  0 | 60  *  *  *  * |  3  3  0  1  0  0  0  0 |  3  6  3  0  3  3  0  0  0  0  0 | 1  3  3  1 0  3  6  3  0 0  0  0  0 0 | 1 1  3  3  1 0 0
.. .. .. .. x.    |  2  0 |  * 60  *  *  * |  0  3  3  0  1  0  0  0 |  0  3  6  3  0  3  3  0  0  0  0 | 0  1  3  3 1  0  3  6  3 0  0  0  0 0 | 1 0  1  3  3 1 0
oo3oo3oo3oo3oo&#x |  1  1 |  *  * 30  *  * |  0  0  0  4  4  0  0  0 |  0  0  0  0  6 12  6  0  0  0  0 | 0  0  0  0 0  4 12 12  4 0  0  0  0 0 | 0 1  4  6  4 1 0
.x .. .. .. ..    |  0  2 |  *  *  * 60  * |  0  0  0  1  0  3  3  0 |  0  0  0  0  3  3  0  3  6  3  0 | 0  0  0  0 0  3  6  3  0 1  3  3  1 0 | 0 1  3  3  1 0 1
.. .. .. .. .x    |  0  2 |  *  *  *  * 60 |  0  0  0  0  1  0  3  3 |  0  0  0  0  0  3  3  0  3  6  3 | 0  0  0  0 0  0  3  6  3 0  1  3  3 1 | 0 0  1  3  3 1 1
------------------+-------+----------------+-------------------------+----------------------------------+---------------------------------------+-----------------
x.3o. .. .. ..    |  3  0 |  3  0  0  0  0 | 60  *  *  *  *  *  *  * |  2  2  0  0  1  0  0  0  0  0  0 | 1  2  1  0 0  2  2  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  1  2  1 0  0  2  2  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  1  0  0  0  0 | 0  0  1  2 1  0  0  2  2 0  0  0  0 0 | 1 0  0  1  2 1 0
xx .. .. .. ..&#x |  2  2 |  1  0  2  1  0 |  *  *  * 60  *  *  *  * |  0  0  0  0  3  3  0  0  0  0  0 | 0  0  0  0 0  3  6  3  0 0  0  0  0 0 | 0 1  3  3  1 0 0
.. .. .. .. xx&#x |  2  2 |  0  1  2  0  1 |  *  *  *  * 60  *  *  * |  0  0  0  0  0  3  3  0  0  0  0 | 0  0  0  0 0  0  3  6  3 0  0  0  0 0 | 0 0  1  3  3 1 0
.x3.o .. .. ..    |  0  3 |  0  0  0  3  0 |  *  *  *  *  * 60  *  * |  0  0  0  0  1  0  0  2  2  0  0 | 0  0  0  0 0  2  2  0  0 1  2  1  0 0 | 0 1  2  1  0 0 1
.x .. .. .. .x    |  0  4 |  0  0  0  2  2 |  *  *  *  *  *  * 90  * |  0  0  0  0  0  1  0  0  2  2  0 | 0  0  0  0 0  0  2  2  0 0  1  2  1 0 | 0 0  1  2  1 0 1
.. .. .. .o3.x    |  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 60 |  0  0  0  0  0  0  1  0  0  2  2 | 0  0  0  0 0  0  0  2  2 0  0  1  2 1 | 0 0  0  1  2 1 1
------------------+-------+----------------+-------------------------+----------------------------------+---------------------------------------+-----------------
x.3o.3o. .. ..      4  0 |  6  0  0  0  0 |  4  0  0  0  0  0  0  0 | 30  *  *  *  *  *  *  *  *  *  * | 1  1  0  0 0  1  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 |  * 60  *  *  *  *  *  *  *  *  * | 0  1  1  0 0  0  1  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 |  *  * 60  *  *  *  *  *  *  *  * | 0  0  1  1 0  0  0  1  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 |  *  *  * 30  *  *  *  *  *  *  * | 0  0  0  1 1  0  0  0  1 0  0  0  0 0 | 1 0  0  0  1 1 0
xx3oo .. .. ..&#x   3  3 |  3  0  3  3  0 |  1  0  0  3  0  1  0  0 |  *  *  *  * 60  *  *  *  *  *  * | 0  0  0  0 0  2  2  0  0 0  0  0  0 0 | 0 1  2  1  0 0 0
xx .. .. .. xx&#x   4  4 |  2  2  4  2  2 |  0  1  0  2  2  0  1  0 |  *  *  *  *  * 90  *  *  *  *  * | 0  0  0  0 0  0  2  2  0 0  0  0  0 0 | 0 0  1  2  1 0 0
.. .. .. oo3xx&#x   3  3 |  0  3  3  0  3 |  0  0  1  0  3  0  0  1 |  *  *  *  *  *  * 60  *  *  *  * | 0  0  0  0 0  0  0  2  2 0  0  0  0 0 | 0 0  0  1  2 1 0
.x3.o3.o .. ..      0  4 |  0  0  0  6  0 |  0  0  0  0  0  4  0  0 |  *  *  *  *  *  *  * 30  *  *  * | 0  0  0  0 0  1  0  0  0 1  1  0  0 0 | 0 1  1  0  0 0 1
.x3.o .. .. .x      0  6 |  0  0  0  6  3 |  0  0  0  0  0  2  3  0 |  *  *  *  *  *  *  *  * 60  *  * | 0  0  0  0 0  0  1  0  0 0  1  1  0 0 | 0 0  1  1  0 0 1
.x .. .. .o3.x      0  6 |  0  0  0  3  6 |  0  0  0  0  0  0  3  2 |  *  *  *  *  *  *  *  *  * 60  * | 0  0  0  0 0  0  0  1  0 0  0  1  1 0 | 0 0  0  1  1 0 1
.. .. .o3.o3.x      0  4 |  0  0  0  0  6 |  0  0  0  0  0  0  0  4 |  *  *  *  *  *  *  *  *  *  * 30 | 0  0  0  0 0  0  0  0  1 0  0  0  1 1 | 0 0  0  0  1 1 1
------------------+-------+----------------+-------------------------+----------------------------------+---------------------------------------+-----------------
x.3o.3o.3o. ..      5  0 | 10  0  0  0  0 | 10  0  0  0  0  0  0  0 |  5  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 |  2  4  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  3  3  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  4  2  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  5  0  0  0  0  0  0  0 | *  *  *  * 6  *  *  *  * *  *  *  * * | 1 0  0  0  0 1 0
xx3oo3oo .. ..&#x   4  4 |  6  0  4  6  0 |  4  0  0  6  0  4  0  0 |  1  0  0  0  4  0  0  1  0  0  0 | *  *  *  * * 30  *  *  * *  *  *  * * | 0 1  1  0  0 0 0
xx3oo .. .. xx&#x   6  6 |  6  3  6  6  3 |  2  3  0  6  3  2  3  0 |  0  1  0  0  2  3  0  0  1  0  0 | *  *  *  * *  * 60  *  * *  *  *  * * | 0 0  1  1  0 0 0
xx .. .. oo3xx&#x   6  6 |  3  6  6  3  6 |  0  3  2  3  6  0  3  2 |  0  0  1  0  0  3  2  0  0  1  0 | *  *  *  * *  *  * 60  * *  *  *  * * | 0 0  0  1  1 0 0
.. .. oo3oo3xx&#x   4  4 |  0  6  4  0  6 |  0  0  4  0  6  0  0  4 |  0  0  0  1  0  0  4  0  0  0  1 | *  *  *  * *  *  *  * 30 *  *  *  * * | 0 0  0  0  1 1 0
.x3.o3.o3.o ..      0  5 |  0  0  0 10  0 |  0  0  0  0  0 10  0  0 |  0  0  0  0  0  0  0  5  0  0  0 | *  *  *  * *  *  *  *  * 6  *  *  * * | 0 1  0  0  0 0 1
.x3.o3.o .. .x      0  8 |  0  0  0 12  4 |  0  0  0  0  0  8  6  0 |  0  0  0  0  0  0  0  2  4  0  0 | *  *  *  * *  *  *  *  * * 15  *  * * | 0 0  1  0  0 0 1
.x3.o .. .o3.x      0  9 |  0  0  0  9  9 |  0  0  0  0  0  3  9  3 |  0  0  0  0  0  0  0  0  3  3  0 | *  *  *  * *  *  *  *  * *  * 20  * * | 0 0  0  1  0 0 1
.x .. .o3.o3.x      0  8 |  0  0  0  4 12 |  0  0  0  0  0  0  6  8 |  0  0  0  0  0  0  0  0  0  4  2 | *  *  *  * *  *  *  *  * *  *  * 15 * | 0 0  0  0  1 0 1
.. .o3.o3.o3.x      0  5 |  0  0  0  0 10 |  0  0  0  0  0  0  0 10 |  0  0  0  0  0  0  0  0  0  0  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 | 30 60 60 30  0  0  0  0  0  0  0 | 6 15 20 15 6  0  0  0  0 0  0  0  0 0 | 1 *  *  *  * * *
xx3oo3oo3oo ..&#x   5  5 | 10  0  5 10  0 | 10  0  0 10  0 10  0  0 |  5  0  0  0 10  0  0  5  0  0  0 | 1  0  0  0 0  5  0  0  0 1  0  0  0 0 | * 6  *  *  * * *
xx3oo3oo .. xx&#x   8  8 | 12  4  8 12  4 |  8  6  0 12  4  8  6  0 |  2  4  0  0  8  6  0  2  4  0  0 | 0  1  0  0 0  2  4  0  0 0  1  0  0 0 | * * 15  *  * * *
xx3oo .. oo3xx&#x   9  9 |  9  9  9  9  9 |  3  9  3  9  9  3  9  3 |  0  3  3  0  3  9  3  0  3  3  0 | 0  0  1  0 0  0  3  3  0 0  0  1  0 0 | * *  * 20  * * *
xx .. oo3oo3xx&#x   8  8 |  4 12  8  4 12 |  0  6  8  4 12  0  6  8 |  0  0  4  2  0  6  8  0  0  4  2 | 0  0  0  1 0  0  0  4  2 0  0  0  1 0 | * *  *  * 15 * *
.. oo3oo3oo3xx&#x   5  5 |  0 10  5  0 10 |  0  0 10  0 10  0  0 10 |  0  0  0  5  0  0 10  0  0  0  5 | 0  0  0  0 1  0  0  0  5 0  0  0  0 1 | * *  *  *  * 6 *
.x3.o3.o3.o3.x      0 30 |  0  0  0 60 60 |  0  0  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 6 15 20 15 6 | * *  *  *  * * 1

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