Acronym	gadtaxhi
Name	great ditetrahedronary hexacosihecatonicosachoron
Cross sections	©
Circumradius	sqrt[3-sqrt(5)] = 0.874032
General of army	hi
Colonel of regiment	gadtaxady
Face vector	600, 3600, 3120, 720
Confer	general polytopal classes: Wythoffian polychora
External links

As abstract polytope gadtaxhi is isomorphic to sidtaxhi, thereby replacing pentagons by pentagrams, resp. gidtid by sidtid. – As such gadtaxhi is a lieutenant.

Incidence matrix according to Dynkin symbol

o3o3o5x3/2*b

. . . .      | 600 |   12 |   6   12 |   4   4
-------------+-----+------+----------+--------
. . . x      |   2 | 3600 |   1    2 |   1   2
-------------+-----+------+----------+--------
. . o5x      |   5 |    5 | 720    * |   0   2
. o . x3/2*b |   3 |    3 |   * 2400 |   1   1
-------------+-----+------+----------+--------
o3o . x3/2*b ♦   4 |    6 |   0    4 | 600   *
. o3o5x3/2*b ♦  20 |   60 |  12   20 |   * 120

o3o3o5/4x3*b

. . .   .    | 600 |   12 |   6   12 |   4   4
-------------+-----+------+----------+--------
. . .   x    |   2 | 3600 |   1    2 |   1   2
-------------+-----+------+----------+--------
. . o5/4x    |   5 |    5 | 720    * |   0   2
. o .   x3*b |   3 |    3 |   * 2400 |   1   1
-------------+-----+------+----------+--------
o3o .   x3*b ♦   4 |    6 |   0    4 | 600   *
. o3o5/4x3*b ♦  20 |   60 |  12   20 |   * 120

o3o3/2o5x3*b

. .   . .    | 600 |   12 |   6   12 |   4   4
-------------+-----+------+----------+--------
. .   . x    |   2 | 3600 |   1    2 |   1   2
-------------+-----+------+----------+--------
. .   o5x    |   5 |    5 | 720    * |   0   2
. o   . x3*b |   3 |    3 |   * 2400 |   1   1
-------------+-----+------+----------+--------
o3o   . x3*b ♦   4 |    6 |   0    4 | 600   *
. o3/2o5x3*b ♦  20 |   60 |  12   20 |   * 120

o3o3/2o5/4x3/2*b

. .   .   .      | 600 |   12 |   6   12 |   4   4
-----------------+-----+------+----------+--------
. .   .   x      |   2 | 3600 |   1    2 |   1   2
-----------------+-----+------+----------+--------
. .   o5/4x      |   5 |    5 | 720    * |   0   2
. o   .   x3/2*b |   3 |    3 |   * 2400 |   1   1
-----------------+-----+------+----------+--------
o3o   .   x3/2*b ♦   4 |    6 |   0    4 | 600   *
. o3/2o5/4x3/2*b ♦  20 |   60 |  12   20 |   * 120

o3/2o3o5x3/2*b

.   . . .      | 600 |   12 |   6   12 |   4   4
---------------+-----+------+----------+--------
.   . . x      |   2 | 3600 |   1    2 |   1   2
---------------+-----+------+----------+--------
.   . o5x      |   5 |    5 | 720    * |   0   2
.   o . x3/2*b |   3 |    3 |   * 2400 |   1   1
---------------+-----+------+----------+--------
o3/2o . x3/2*b ♦   4 |    6 |   0    4 | 600   *
.   o3o5x3/2*b ♦  20 |   60 |  12   20 |   * 120

o3/2o3o5/4x3*b

.   . .   .    | 600 |   12 |   6   12 |   4   4
---------------+-----+------+----------+--------
.   . .   x    |   2 | 3600 |   1    2 |   1   2
---------------+-----+------+----------+--------
.   . o5/4x    |   5 |    5 | 720    * |   0   2
.   o .   x3*b |   3 |    3 |   * 2400 |   1   1
---------------+-----+------+----------+--------
o3/2o .   x3*b ♦   4 |    6 |   0    4 | 600   *
.   o3o5/4x3*b ♦  20 |   60 |  12   20 |   * 120

o3/2o3/2o5x3*b

.   .   . .    | 600 |   12 |   6   12 |   4   4
---------------+-----+------+----------+--------
.   .   . x    |   2 | 3600 |   1    2 |   1   2
---------------+-----+------+----------+--------
.   .   o5x    |   5 |    5 | 720    * |   0   2
.   o   . x3*b |   3 |    3 |   * 2400 |   1   1
---------------+-----+------+----------+--------
o3/2o   . x3*b ♦   4 |    6 |   0    4 | 600   *
.   o3/2o5x3*b ♦  20 |   60 |  12   20 |   * 120

o3/2o3/2o5/4x3/2*b

.   .   .   .      | 600 |   12 |   6   12 |   4   4
-------------------+-----+------+----------+--------
.   .   .   x      |   2 | 3600 |   1    2 |   1   2
-------------------+-----+------+----------+--------
.   .   o5/4x      |   5 |    5 | 720    * |   0   2
.   o   .   x3/2*b |   3 |    3 |   * 2400 |   1   1
-------------------+-----+------+----------+--------
o3/2o   .   x3/2*b ♦   4 |    6 |   0    4 | 600   *
.   o3/2o5/4x3/2*b ♦  20 |   60 |  12   20 |   * 120