Acronym	gax
Name	grand hexacosachoron
Cross sections	©
Circumradius	(sqrt(5)-1)/2 = 0.618034
Inradius	sqrt[(9-4 sqrt(5))/8] = 0.083463
General of army	ex
Colonel of regiment	gishi
Dual	gogishi
Confer	Grünbaumian relatives: gax+gashi+120gid   2gax   gax+gofix   related scaliform: birgax   general polytopal classes: regular
External links

As abstract polytope gax is isomorphic to ex, thereby replacing pentagrammal edge figures by pentagonal ones resp. replacing gike vertex figures by ike ones. – As such gax is a lieutenant.

Incidence matrix according to Dynkin symbol

x3o3o5/2o

. . .   . | 120 ♦  12 |   30 |  20
----------+-----+-----+------+----
x . .   . |   2 | 720 |    5 |   5
----------+-----+-----+------+----
x3o .   . |   3 |   3 | 1200 |   2
----------+-----+-----+------+----
x3o3o   . ♦   4 |   6 |    4 | 600

x3o3o5/3o

. . .   . | 120 ♦  12 |   30 |  20
----------+-----+-----+------+----
x . .   . |   2 | 720 |    5 |   5
----------+-----+-----+------+----
x3o .   . |   3 |   3 | 1200 |   2
----------+-----+-----+------+----
x3o3o   . ♦   4 |   6 |    4 | 600

x3o3/2o5/2o

. .   .   . | 120 ♦  12 |   30 |  20
------------+-----+-----+------+----
x .   .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3o   .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3o3/2o   . ♦   4 |   6 |    4 | 600

x3o3/2o5/3o

. .   .   . | 120 ♦  12 |   30 |  20
------------+-----+-----+------+----
x .   .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3o   .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3o3/2o   . ♦   4 |   6 |    4 | 600

x3/2o3o5/2o

.   . .   . | 120 ♦  12 |   30 |  20
------------+-----+-----+------+----
x   . .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3/2o .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3/2o3o   . ♦   4 |   6 |    4 | 600

x3/2o3o5/3o

.   . .   . | 120 ♦  12 |   30 |  20
------------+-----+-----+------+----
x   . .   . |   2 | 720 |    5 |   5
------------+-----+-----+------+----
x3/2o .   . |   3 |   3 | 1200 |   2
------------+-----+-----+------+----
x3/2o3o   . ♦   4 |   6 |    4 | 600

x3/2o3/2o5/2o

.   .   .   . | 120 ♦  12 |   30 |  20
--------------+-----+-----+------+----
x   .   .   . |   2 | 720 |    5 |   5
--------------+-----+-----+------+----
x3/2o   .   . |   3 |   3 | 1200 |   2
--------------+-----+-----+------+----
x3/2o3/2o   . ♦   4 |   6 |    4 | 600

x3/2o3/2o5/3o

.   .   .   . | 120 ♦  12 |   30 |  20
--------------+-----+-----+------+----
x   .   .   . |   2 | 720 |    5 |   5
--------------+-----+-----+------+----
x3/2o   .   . |   3 |   3 | 1200 |   2
--------------+-----+-----+------+----
x3/2o3/2o   . ♦   4 |   6 |    4 | 600