Acronym	xhi
Name	hexacosihecatonicosachoron, bitruncated hecatonicosachoron, bitruncated hexacosachoron
Cross sections	©
Circumradius	sqrt[(59+25 sqrt(5))/2] = 7.579634
Vertex figure	©
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: ti tut xhi 120 600 )
Dihedral angles	at {3} between tut and tut:   arccos[-(1+3 sqrt(5))/8] = 164.477512° at {6} between ti and tut:   arccos(-sqrt[7+3 sqrt(5)]/4) = 157.761244° at {5} between ti and ti:   144°
Face vector	3600, 7200, 4320, 720
Confer	Grünbaumian relatives: 2xhi   decompositions: srahi || xhi   ambification: rexhi   general polytopal classes: Wythoffian polychora
External links

As abstract polytope xhi is isomorphic to gixhi, thereby replacing the pentagons by pentagrams, resp. replacing ti by tiggy.

Note that xhi can be thought of as the external blend of 1 srahi + 600 octatuts + 1200 triddips + 120 sridaties. This decomposition is described as the degenerate segmentoteron oo3xx3ox5xo&#x.

Incidence matrix according to Dynkin symbol

o3x3x5o

. . . . | 3600 |    2    2 |    1    4   1 |   2   2
--------+------+-----------+---------------+--------
. x . . |    2 | 3600    * |    1    2   0 |   2   1
. . x . |    2 |    * 3600 |    0    2   1 |   1   2
--------+------+-----------+---------------+--------
o3x . . |    3 |    3    0 | 1200    *   * |   2   0
. x3x . |    6 |    3    3 |    * 2400   * |   1   1
. . x5o |    5 |    0    5 |    *    * 720 |   0   2
--------+------+-----------+---------------+--------
o3x3x . ♦   12 |   12    6 |    4    4   0 | 600   *
. x3x5o ♦   60 |   30   60 |    0   20  12 |   * 120

snubbed forms: o3β3x5o, o3x3β5o, o3β3β5o

o3x3x5/4o

. . .   . | 3600 |    2    2 |    1    4   1 |   2   2
----------+------+-----------+---------------+--------
. x .   . |    2 | 3600    * |    1    2   0 |   2   1
. . x   . |    2 |    * 3600 |    0    2   1 |   1   2
----------+------+-----------+---------------+--------
o3x .   . |    3 |    3    0 | 1200    *   * |   2   0
. x3x   . |    6 |    3    3 |    * 2400   * |   1   1
. . x5/4o |    5 |    0    5 |    *    * 720 |   0   2
----------+------+-----------+---------------+--------
o3x3x   . ♦   12 |   12    6 |    4    4   0 | 600   *
. x3x5/4o ♦   60 |   30   60 |    0   20  12 |   * 120

o3/2x3x5o

.   . . . | 3600 |    2    2 |    1    4   1 |   2   2
----------+------+-----------+---------------+--------
.   x . . |    2 | 3600    * |    1    2   0 |   2   1
.   . x . |    2 |    * 3600 |    0    2   1 |   1   2
----------+------+-----------+---------------+--------
o3/2x . . |    3 |    3    0 | 1200    *   * |   2   0
.   x3x . |    6 |    3    3 |    * 2400   * |   1   1
.   . x5o |    5 |    0    5 |    *    * 720 |   0   2
----------+------+-----------+---------------+--------
o3/2x3x . ♦   12 |   12    6 |    4    4   0 | 600   *
.   x3x5o ♦   60 |   30   60 |    0   20  12 |   * 120

o3/2x3x5/4o

.   . .   . | 3600 |    2    2 |    1    4   1 |   2   2
------------+------+-----------+---------------+--------
.   x .   . |    2 | 3600    * |    1    2   0 |   2   1
.   . x   . |    2 |    * 3600 |    0    2   1 |   1   2
------------+------+-----------+---------------+--------
o3/2x .   . |    3 |    3    0 | 1200    *   * |   2   0
.   x3x   . |    6 |    3    3 |    * 2400   * |   1   1
.   . x5/4o |    5 |    0    5 |    *    * 720 |   0   2
------------+------+-----------+---------------+--------
o3/2x3x   . ♦   12 |   12    6 |    4    4   0 | 600   *
.   x3x5/4o ♦   60 |   30   60 |    0   20  12 |   * 120