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 120600
)
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°
Confer
Grünbaumian relatives:
2xhi  
decompositions:
srahi || xhi  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

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

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