Acronym	taz
Name	truncated hecatonicosoctaexon, truncated heptacross, equatorial cross-section of zee-first tek
Circumradius	sqrt(5/2) = 1.581139
Inradius wrt. gee	sqrt(2) = 1.414214
Inradius wrt. til	3/sqrt(14) = 0.801784
Coordinates	(2/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume	218 sqrt(2)/63 = 4.893628
Surface	(7+722 sqrt(7))/45 = 42.605165
Dihedral angles (at margins)	at tix between til and til:   arccos(-5/7) = 135.584691° at hix between gee and til:   arccos[-1/sqrt(7)] = 112.207654°
Face vector	168, 924, 2520, 3920, 3360, 1344, 142
Confer	general polytopal classes: Wythoffian polyexa   analogs: truncated orthoplex tOn
External links

Incidence matrix according to Dynkin symbol

x3x3o3o3o3o4o

. . . . . . . | 168 |  1  10 |  10   40 |  40   80 |  80   80 |  80  32 |  32  1
--------------+-----+--------+----------+----------+----------+---------+-------
x . . . . . . |   2 | 84   * ♦  10    0 |  40    0 |  80    0 |  80   0 |  32  0
. x . . . . . |   2 |  * 840 |   1    8 |   8   24 |  24   32 |  32  16 |  16  1
--------------+-----+--------+----------+----------+----------+---------+-------
x3x . . . . . |   6 |  3   3 | 280    * ♦   8    0 |  24    0 |  32   0 |  16  0
. x3o . . . . |   3 |  0   3 |   * 2240 |   1    6 |   6   12 |  12   8 |   8  1
--------------+-----+--------+----------+----------+----------+---------+-------
x3x3o . . . . ♦  12 |  6  12 |   4    4 | 560    * ♦   6    0 |  12   0 |   8  0
. x3o3o . . . ♦   4 |  0   6 |   0    4 |   * 3360 |   1    4 |   4   4 |   4  1
--------------+-----+--------+----------+----------+----------+---------+-------
x3x3o3o . . . ♦  20 | 10  30 |  10   20 |   5    5 | 672    * |   4   0 |   4  0
. x3o3o3o . . ♦   5 |  0  10 |   0   10 |   0    5 |   * 2688 |   1   2 |   2  1
--------------+-----+--------+----------+----------+----------+---------+-------
x3x3o3o3o . . ♦  30 | 15  60 |  20   60 |  15   30 |   6    6 | 448   * |   2  0
. x3o3o3o3o . ♦   6 |  0  15 |   0   20 |   0   15 |   0    6 |   * 896 |   1  1
--------------+-----+--------+----------+----------+----------+---------+-------
x3x3o3o3o3o . ♦  42 | 21 105 |  35  140 |  35  105 |  21   42 |   7   7 | 128  *
. x3o3o3o3o4o ♦  12 |  0  60 |   0  160 |   0  240 |   0  192 |   0  64 |   * 14

x3x3o3o3o3o4/3o

. . . . . .   . | 168 |  1  10 |  10   40 |  40   80 |  80   80 |  80  32 |  32  1
----------------+-----+--------+----------+----------+----------+---------+-------
x . . . . .   . |   2 | 84   * ♦  10    0 |  40    0 |  80    0 |  80   0 |  32  0
. x . . . .   . |   2 |  * 840 |   1    8 |   8   24 |  24   32 |  32  16 |  16  1
----------------+-----+--------+----------+----------+----------+---------+-------
x3x . . . .   . |   6 |  3   3 | 280    * ♦   8    0 |  24    0 |  32   0 |  16  0
. x3o . . .   . |   3 |  0   3 |   * 2240 |   1    6 |   6   12 |  12   8 |   8  1
----------------+-----+--------+----------+----------+----------+---------+-------
x3x3o . . .   . ♦  12 |  6  12 |   4    4 | 560    * ♦   6    0 |  12   0 |   8  0
. x3o3o . .   . ♦   4 |  0   6 |   0    4 |   * 3360 |   1    4 |   4   4 |   4  1
----------------+-----+--------+----------+----------+----------+---------+-------
x3x3o3o . .   . ♦  20 | 10  30 |  10   20 |   5    5 | 672    * |   4   0 |   4  0
. x3o3o3o .   . ♦   5 |  0  10 |   0   10 |   0    5 |   * 2688 |   1   2 |   2  1
----------------+-----+--------+----------+----------+----------+---------+-------
x3x3o3o3o .   . ♦  30 | 15  60 |  20   60 |  15   30 |   6    6 | 448   * |   2  0
. x3o3o3o3o   . ♦   6 |  0  15 |   0   20 |   0   15 |   0    6 |   * 896 |   1  1
----------------+-----+--------+----------+----------+----------+---------+-------
x3x3o3o3o3o   . ♦  42 | 21 105 |  35  140 |  35  105 |  21   42 |   7   7 | 128  *
. x3o3o3o3o4/3o ♦  12 |  0  60 |   0  160 |   0  240 |   0  192 |   0  64 |   * 14

o3o3o *b3o3o3x3x

. . .    . . . . | 168 |  10  1 |   40  10 |   80  40 |   80  80 |  16  16  80 |  1 16 16
-----------------+-----+--------+----------+----------+----------+-------------+---------
. . .    . . x . |   2 | 840  * |    8   1 |   24   8 |   32  24 |   8   8  32 |  1  8  8
. . .    . . . x |   2 |   * 84 ♦    0  10 |    0  40 |    0  80 |   0   0  80 |  0 16 16
-----------------+-----+--------+----------+----------+----------+-------------+---------
. . .    . o3x . |   3 |   3  0 | 2240   * |    6   1 |   12   6 |   4   4  12 |  1  4  4
. . .    . . x3x |   6 |   3  3 |    * 280 ♦    0   8 |    0  24 |   0   0  32 |  0  8  8
-----------------+-----+--------+----------+----------+----------+-------------+---------
. . .    o3o3x . ♦   4 |   6  0 |    4   0 | 3360   * |    4   1 |   2   2   4 |  1  2  2
. . .    . o3x3x ♦  12 |  12  6 |    4   4 |    * 560 ♦    0   6 |   0   0  12 |  0  4  4
-----------------+-----+--------+----------+----------+----------+-------------+---------
. o . *b3o3o3x . ♦   5 |  10  0 |   10   0 |    5   0 | 2688   * |   1   1   1 |  1  1  1
. . .    o3o3x3x ♦  20 |  30 10 |   20  10 |    5   5 |    * 672 |   0   0   4 |  0  2  2
-----------------+-----+--------+----------+----------+----------+-------------+---------
o3o . *b3o3o3x . ♦   6 |  15  0 |   20   0 |   15   0 |    6   0 | 448   *   * |  1  1  0
. o3o *b3o3o3x . ♦   6 |  15  0 |   20   0 |   15   0 |    6   0 |   * 448   * |  1  0  1
. o . *b3o3o3x3x ♦  30 |  60 15 |   60  20 |   30  15 |    6   6 |   *   * 448 |  0  1  1
-----------------+-----+--------+----------+----------+----------+-------------+---------
o3o3o *b3o3o3x . ♦  12 |  60  0 |  160   0 |  240   0 |  192   0 |  32  32   0 | 14  *  *
o3o . *b3o3o3x3x ♦  42 | 105 21 |  140  35 |  105  35 |   42  21 |   7   0   7 |  * 64  *
. o3o *b3o3o3x3x ♦  42 | 105 21 |  140  35 |  105  35 |   42  21 |   0   7   7 |  *  * 64