Acronym	grix
Name	great rhombated hexacosachoron, cantitruncated hexacosachoron
Cross sections	©
Circumradius	sqrt[43+18 sqrt(5)] = 9.124101
Vertex figure	©
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: pip ti toe grix 720 120 600 )
Dihedral angles	at {4} between pip and toe:   arccos(-sqrt[(5+2 sqrt(5))/10]) = 166.717474° at {6} between toe and toe:   arccos[-(1+3 sqrt(5))/8] = 164.477512° at {5} between pip and ti:   162° at {6} between ti and toe:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244°
Face vector	7200, 14400, 8640, 1440
Confer	Grünbaumian relatives: 2grix   decompositions: prahi || grix   general polytopal classes: Wythoffian polychora
External links

As abstract polytope grix is isomorphic to graggix, thereby replacing the pentagons by pentagrams, resp. replacing ti by tiggy and pip by stip.

Note that grix can be thought of as the external blend of 1 prahi + 600 tutatoes + 1200 thiddips + 720 pappips + 120 sridaties. This decomposition is described as the degenerate segmentoteron xx3xx3ox5xo&#x.

Incidence matrix according to Dynkin symbol

x3x3x5o

. . . . | 7200 |    1    1    2 |    1    2    2    1 |   2   1   1
--------+------+----------------+---------------------+------------
x . . . |    2 | 3600    *    * |    1    2    0    0 |   2   1   0
. x . . |    2 |    * 3600    * |    1    0    2    0 |   2   0   1
. . x . |    2 |    *    * 7200 |    0    1    1    1 |   1   1   1
--------+------+----------------+---------------------+------------
x3x . . |    6 |    3    3    0 | 1200    *    *    * |   2   0   0
x . x . |    4 |    2    0    2 |    * 3600    *    * |   1   1   0
. x3x . |    6 |    0    3    3 |    *    * 2400    * |   1   0   1
. . x5o |    5 |    0    0    5 |    *    *    * 1440 |   0   1   1
--------+------+----------------+---------------------+------------
x3x3x . ♦   24 |   12   12   12 |    4    6    4    0 | 600   *   *
x . x5o ♦   10 |    5    0   10 |    0    5    0    2 |   * 720   *
. x3x5o ♦   60 |    0   30   60 |    0    0   20   12 |   *   * 120

snubbed forms: β3x3x5o, x3β3x5o, x3x3β5o, β3β3x5o, β3x3β5o, x3β3β5o, β3β3β5o

x3x3x5/4o

. . .   . | 7200 |    1    1    2 |    1    2    2    1 |   2   1   1
----------+------+----------------+---------------------+------------
x . .   . |    2 | 3600    *    * |    1    2    0    0 |   2   1   0
. x .   . |    2 |    * 3600    * |    1    0    2    0 |   2   0   1
. . x   . |    2 |    *    * 7200 |    0    1    1    1 |   1   1   1
----------+------+----------------+---------------------+------------
x3x .   . |    6 |    3    3    0 | 1200    *    *    * |   2   0   0
x . x   . |    4 |    2    0    2 |    * 3600    *    * |   1   1   0
. x3x   . |    6 |    0    3    3 |    *    * 2400    * |   1   0   1
. . x5/4o |    5 |    0    0    5 |    *    *    * 1440 |   0   1   1
----------+------+----------------+---------------------+------------
x3x3x   . ♦   24 |   12   12   12 |    4    6    4    0 | 600   *   *
x . x5/4o ♦   10 |    5    0   10 |    0    5    0    2 |   * 720   *
. x3x5/4o ♦   60 |    0   30   60 |    0    0   20   12 |   *   * 120