Acronym	gax, apT
Name	grand hexacosachoron, aggrandized polytetrahedron
Cross sections	©
Circumradius	(sqrt(5)-1)/2 = 0.618034
Inradius	sqrt[(9-4 sqrt(5))/8] = 0.083463
Density	191
General of army	ex
Colonel of regiment	gishi
Dual	gogishi
Dihedral angles	at {3} between tet and tet:   arccos[(3 sqrt(5)-1)/8] = 44.477512°
Face vector	120, 720, 1200, 600
Confer	Grünbaumian relatives: gax+gashi+120gid   2gax   gax+gofix   related scaliform: birgax   gisp   gypasp   general polytopal classes: Wythoffian polychora   regular   noble polytopes
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