qrax

Acronym	qrax
Name	quasirhombated hexeract
Circumradius	sqrt[(7-4 sqrt(2))/2] = 0.819496
Inradius wrt. quarn	(sqrt(2)-1)/2 = 0.207107
Inradius wrt. penp	sqrt[(57-40 sqrt(2))/20] = 0.146877
Inradius wrt. rix	sqrt[(17-12 sqrt(2))/6] = 0.0700443
Coordinates	((sqrt(2)-1)/2, (sqrt(2)-1)/2, (sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2) & all permutations, all changes of sign
Volume	[3141 sqrt(2)-4426]/45 = 0.356551
Dihedral angles (at margins)	at qrit between quarn and quarn: 90° at rap between quarn and rix: arccos[1/sqrt(6)] = 65.905157° at tepe between penp and quarn: arccos[1/sqrt(5)] = 63.434949° at pen between penp and rix: arccos[sqrt(5/6)] = 24.094843°
Face vector	960, 4800, 7280, 4960, 1788, 268
Confer	general polytopal classes: Wythoffian polypeta analogs: quasirhombated hypercube qrbC_n

As abstract polytope qrax is isomorphic to srox, thereby replacing querco by sirco, qrit by srit, and quarn by sirn. – As such qrax is a lieutenant.

Incidence matrix according to Dynkin symbol

o3o3o3x3o4/3x

. . . . .   . | 960 |    8   2 |   12    4    8   1 |    8   6   12   4 |   2   4   8  6 |  1   2  4
--------------+-----+----------+--------------------+-------------------+----------------+----------
. . . x .   . |   2 | 3840   * |    3    1    1   0 |    3   3    3   1 |   1   3   3  3 |  1   1  3
. . . . .   x |   2 |    * 960 |    0    0    4   1 |    0   0    6   4 |   0   0   4  6 |  0   1  4
--------------+-----+----------+--------------------+-------------------+----------------+----------
. . o3x .   . |   3 |    3   0 | 3840    *    *   * |    2   1    1   0 |   1   2   2  1 |  1   1  2
. . . x3o   . |   3 |    3   0 |    * 1280    *   * |    0   3    0   1 |   0   3   0  3 |  1   0  3
. . . x .   x |   4 |    2   2 |    *    * 1920   * |    0   0    3   1 |   0   0   3  3 |  0   1  3
. . . . o4/3x |   4 |    0   4 |    *    *    * 240 ♦    0   0    0   4 |   0   0   0  6 |  0   0  4
--------------+-----+----------+--------------------+-------------------+----------------+----------
. o3o3x .   . ♦   4 |    6   0 |    4    0    0   0 | 1920   *    *   * |   1   1   1  0 |  1   1  1
. . o3x3o   . ♦   6 |   12   0 |    4    4    0   0 |    * 960    *   * |   0   2   0  1 |  1   0  2
. . o3x .   x ♦   6 |    6   3 |    2    0    3   0 |    *   * 1920   * |   0   0   2  1 |  0   1  2
. . . x3o4/3x ♦  24 |   24  24 |    0    8   12   6 |    *   *    * 160 |   0   0   0  3 |  0   0  3
--------------+-----+----------+--------------------+-------------------+----------------+----------
o3o3o3x .   . ♦   5 |   10   0 |   10    0    0   0 |    5   0    0   0 | 384   *   *  * |  1   1  0
. o3o3x3o   . ♦  10 |   30   0 |   20   10    0   0 |    5   5    0   0 |   * 384   *  * |  1   0  1
. o3o3x .   x ♦   8 |   12   4 |    8    0    6   0 |    2   0    4   0 |   *   * 960  * |  0   1  1
. . o3x3o4/3x ♦  96 |  192  96 |   64   64   96  24 |    0  16   32   8 |   *   *   * 60 |  0   0  2
--------------+-----+----------+--------------------+-------------------+----------------+----------
o3o3o3x3o   . ♦  15 |   60   0 |   60   20    0   0 |   30  15    0   0 |   6   6   0  0 | 64   *  *
o3o3o3x .   x ♦  10 |   20   5 |   20    0   10   0 |   10   0   10   0 |   2   0   5  0 |  * 192  *
. o3o3x3o4/3x ♦ 320 |  960 320 |  640  320  480  80 |  160 160  320  40 |   0  32  80 10 |  *   * 12

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