quitoxog

Acronym	quitoxog
Name	quasiterated hexeractihexacontatetrapeton
Circumradius	sqrt[2-1/sqrt(2)] = 1.137055
Inradius wrt. hix	-[3 sqrt(2)-1]/sqrt(12) = -0.936070
Inradius wrt. penp	[5-sqrt(2)]/sqrt(20) = 0.801806
Inradius wrt. squatet	-[2 sqrt(2)-1]/sqrt(8) = -0.646447
Inradius wrt. tracube	[3-sqrt(2)]/sqrt(12) = 0.457777
Inradius wrt. pent	-(sqrt(2)-1)/2 = -0.207107
Coordinates	((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign
Volume	[833-579 sqrt(2)]/45 = 0.314897
Surface	[1080+300 sqrt(2)+601 sqrt(3)+30 sqrt(5)]/15 = 174.153910
Dihedral angles (at margins)	at tes between pent and pent: 45° at tes between pent and tracube: arccos(sqrt(2/3)) = 35.264390° at tisdip between squatet and tracube: 30° at tepe between penp and squatet: arccos[2/sqrt(5)] = 26.565051° at pen between hix and penp: arccos[sqrt(5/6)] = 24.094843°
Face vector	384, 1920, 4160, 4800, 2904, 728
Confer	general polytopal classes: Wythoffian polypeta analogs: quasiexpanded hypercube qeC_n

As abstract polytope quitoxog is isomorphic to stoxog.

Incidence matrix according to Dynkin symbol

x3o3o3o3o4/3x

. . . . .   . | 384 |   5   5 |   10   20  10 |  10   30   30  10 |   5  20  30  20   5 |  1   5  10  10  5  1
--------------+-----+---------+---------------+-------------------+---------------------+---------------------
x . . . .   . |   2 | 960   * |    4    4   0 |   6   12    6   0 |   4  12  12   4   0 |  1   4   6   4  1  0
. . . . .   x |   2 |   * 960 |    0    4   4 |   0    6   12   6 |   0   4  12  12   4 |  0   1   4   6  4  1
--------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o . . .   . |   3 |   3   0 | 1280    *   * |   3    3    0   0 |   3   6   3   0   0 |  1   3   3   1  0  0
x . . . .   x |   4 |   2   2 |    * 1920   * |   0    3    3   0 |   0   3   6   3   0 |  0   1   3   3  1  0
. . . . o4/3x |   4 |   0   4 |    *    * 960 |   0    0    3   3 |   0   0   3   6   3 |  0   0   1   3  3  1
--------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o3o . .   . ♦   4 |   6   0 |    4    0   0 | 960    *    *   * |   2   2   0   0   0 |  1   2   1   0  0  0
x3o . . .   x ♦   6 |   6   3 |    2    3   0 |   * 1920    *   * |   0   2   2   0   0 |  0   1   2   1  0  0
x . . . o4/3x ♦   8 |   4   8 |    0    4   2 |   *    * 1440   * |   0   0   2   2   0 |  0   0   1   2  1  0
. . . o3o4/3x ♦   8 |   0  12 |    0    0   6 |   *    *    * 480 |   0   0   0   2   2 |  0   0   0   1  2  1
--------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o3o3o .   . ♦   5 |  10   0 |   10    0   0 |   5    0    0   0 | 384   *   *   *   * |  1   1   0   0  0  0
x3o3o . .   x ♦   8 |  12   4 |    8    6   0 |   2    4    0   0 |   * 960   *   *   * |  0   1   1   0  0  0
x3o . . o4/3x ♦  12 |  12  12 |    4   12   3 |   0    4    3   0 |   *   * 960   *   * |  0   0   1   1  0  0
x . . o3o4/3x ♦  16 |   8  24 |    0   12  12 |   0    0    6   2 |   *   *   * 480   * |  0   0   0   1  1  0
. . o3o3o4/3x ♦  16 |   0  32 |    0    0  24 |   0    0    0   8 |   *   *   *   * 120 |  0   0   0   0  1  1
--------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o3o3o3o   . ♦   6 |  15   0 |   20    0   0 |  15    0    0   0 |   6   0   0   0   0 | 64   *   *   *  *  *
x3o3o3o .   x ♦  10 |  20   5 |   20   10   0 |  10   10    0   0 |   2   5   0   0   0 |  * 192   *   *  *  *
x3o3o . o4/3x ♦  16 |  24  16 |   16   24   4 |   4   16    6   0 |   0   4   4   0   0 |  *   * 240   *  *  *
x3o . o3o4/3x ♦  24 |  24  36 |    8   36  18 |   0   12   18   3 |   0   0   6   3   0 |  *   *   * 160  *  *
x . o3o3o4/3x ♦  32 |  16  64 |    0   32  48 |   0    0   24  16 |   0   0   0   8   2 |  *   *   *   * 60  *
. o3o3o3o4/3x ♦  32 |   0  80 |    0    0  80 |   0    0    0  40 |   0   0   0   0  10 |  *   *   *   *  * 12

top of page