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°
Confer
Grünbaumian relatives:
gax+gashi+120gid   2gax   gax+gofix  
related scaliform:
birgax   gisp   gypasp  
general polytopal classes:
regular   noble polytopes  
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   nan ma

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

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