Acronym tragittith
Name (triangle,gittith)-duoprism
Circumradius sqrt[(11-3 sqrt(2))/6] = 1.061238
Face vector 192, 768, 1048, 696, 235, 35
Confer
general polytopal classes:
Wythoffian polypeta  

As abstract polytope tragittith is isomorphic to trasteth, thereby replacing octagrams by octagons, resp. stop by op and gocco by socco, resp. tistodip by todip, goccope by soccope and gittith by steth, resp. tragocco by trasocco and gittithip by stethip.


Incidence matrix according to Dynkin symbol

x3o o3o3x4/3x4*d

. . . . .   .    | 192 |   2   3   3 |  1   6   6   3   3  3 |  3  3   6   6  6  1  1  3 |  3  3  3  2  2  6 1 |  1 1 3 2
-----------------+-----+-------------+-----------------------+---------------------------+---------------------+---------
x . . . .   .    |   2 | 192   *   * |  1   3   3   0   0  0 |  3  3   3   3  3  0  0  0 |  3  3  3  1  1  3 0 |  1 1 3 1
. . . . x   .    |   2 |   * 288   * |  0   2   0   2   0  1 |  1  0   4   0  2  1  0  2 |  2  0  1  2  0  4 1 |  1 0 2 2
. . . . .   x    |   2 |   *   * 288 |  0   0   2   0   2  1 |  0  1   0   4  2  0  1  2 |  0  2  1  0  2  4 1 |  0 1 2 2
-----------------+-----+-------------+-----------------------+---------------------------+---------------------+---------
x3o . . .   .    |   3 |   3   0   0 | 64   *   *   *   *  * |  3  3   0   0  0  0  0  0 |  3  3  3  0  0  0 0 |  1 1 3 0
x . . . x   .    |   4 |   2   2   0 |  * 288   *   *   *  * |  1  0   2   0  1  0  0  0 |  2  0  1  1  0  2 0 |  1 0 2 1
x . . . .   x    |   4 |   2   0   2 |  *   * 288   *   *  * |  0  1   0   2  1  0  0  0 |  0  2  1  0  1  2 0 |  0 1 2 1
. . . o3x   .    |   3 |   0   3   0 |  *   *   * 192   *  * |  0  0   2   0  0  1  0  1 |  1  0  0  2  0  2 1 |  1 0 1 2
. . . o .   x4*d |   4 |   0   0   4 |  *   *   *   * 144  * |  0  0   0   2  0  0  1  1 |  0  1  0  0  2  2 1 |  0 1 1 2
. . . . x4/3x    |   8 |   0   4   4 |  *   *   *   *   * 72 |  0  0   0   0  2  0  0  2 |  0  0  1  0  0  4 1 |  0 0 2 2
-----------------+-----+-------------+-----------------------+---------------------------+---------------------+---------
x3o . . x   .       6 |   6   3   0 |  2   3   0   0   0  0 | 96  *   *   *  *  *  *  * |  2  0  1  0  0  0 0 |  1 0 2 0
x3o . . .   x       6 |   6   0   3 |  2   0   3   0   0  0 |  * 96   *   *  *  *  *  * |  0  2  1  0  0  0 0 |  0 1 2 0
x . . o3x   .       6 |   3   6   0 |  0   3   0   2   0  0 |  *  * 192   *  *  *  *  * |  1  0  0  1  0  1 0 |  1 0 1 1
x . . o .   x4*d    8 |   4   0   8 |  0   0   4   0   2  0 |  *  *   * 144  *  *  *  * |  0  1  0  0  1  1 0 |  0 1 1 1
x . . . x4/3x      16 |   8   8   8 |  0   4   4   0   0  2 |  *  *   *   * 72  *  *  * |  0  0  1  0  0  2 0 |  0 0 2 1
. . o3o3x   .       4 |   0   6   0 |  0   0   0   4   0  0 |  *  *   *   *  * 48  *  * |  0  0  0  2  0  0 1 |  1 0 0 2
. . o3o .   x4*d    8 |   0   0  12 |  0   0   0   0   6  0 |  *  *   *   *  *  * 24  * |  0  0  0  0  2  0 1 |  0 1 0 2
. . . o3x4/3x4*d   24 |   0  24  24 |  0   0   0   8   6  6 |  *  *   *   *  *  *  * 24 |  0  0  0  0  0  2 1 |  0 0 1 2
-----------------+-----+-------------+-----------------------+---------------------------+---------------------+---------
x3o . o3x   .       9 |   9   9   0 |  3   9   0   3   0  0 |  3  0   3   0  0  0  0  0 | 64  *  *  *  *  * * |  1 0 1 0
x3o . o .   x4*d   12 |  12   0  12 |  4   0  12   0   3  0 |  0  4   0   3  0  0  0  0 |  * 48  *  *  *  * * |  0 1 1 0
x3o . . x4/3x      24 |  24  12  12 |  8  12  12   0   0  3 |  4  4   0   0  3  0  0  0 |  *  * 24  *  *  * * |  0 0 2 0
x . o3o3x   .       8 |   4  12   0 |  0   6   0   8   0  0 |  0  0   4   0  0  2  0  0 |  *  *  * 48  *  * * |  1 0 0 1
x . o3o .   x4*d   16 |   8   0  24 |  0   0  12   0  12  0 |  0  0   0   6  0  0  2  0 |  *  *  *  * 24  * * |  0 1 0 1
x . . o3x4/3x4*d   48 |  24  48  48 |  0  24  24  16  12 12 |  0  0   8   6  6  0  0  2 |  *  *  *  *  * 24 * |  0 0 1 1
. . o3o3x4/3x4*d   64 |   0  96  96 |  0   0   0  64  48 24 |  0  0   0   0  0 16  8  8 |  *  *  *  *  *  * 3 |  0 0 0 2
-----------------+-----+-------------+-----------------------+---------------------------+---------------------+---------
x3o o3o3x   .      12 |  12  18   0 |  4  18   0  12   0  0 |  6  0  12   0  0  3  0  0 |  4  0  0  3  0  0 0 | 16 * * *
x3o o3o .   x4*d   24 |  24   0  36 |  8   0  36   0  18  0 |  0 12   0  18  0  0  3  0 |  0  6  0  0  3  0 0 |  * 8 * *
x3o . o3x4/3x4*d   72 |  72  72  72 | 24  72  72  24  18 18 | 24 24  24  18 18  0  0  3 |  8  6  6  0  0  3 0 |  * * 8 *
x . o3o3x4/3x4*d  128 |  64 192 192 |  0  96  96 128  96 48 |  0  0  64  48 24 32 16 16 |  0  0  0 16  8  8 2 |  * * * 3

© 2004-2024
top of page