Acronym gittith
Name great tesseractitesseractihexadecachoron
Cross sections
 ©
Circumradius sqrt[(3-sqrt(2))/2] = 0.890446
Inradius
wrt. tet
[2 sqrt(2)-1]/sqrt(8) = 0.646447
Inradius
wrt. gocco
1/2 = 0.5
Inradius
wrt. cube
(sqrt(2)-1)/2 = 0.207107
Coordinates ((sqrt(2)-1)/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume [24 sqrt(2)-19]/6 = 2.490188
Surface [68 sqrt(2)-24]/3 = 24.055507
General of army tat
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: cube gocco groh querco stop tet trip
quidpith 3200001632
picnut 248000032
gittifcoth 240080160
gaquipadah 1600081632
gittith 88000160
gahfipto 80080032
gnappoth 008001632
& others)
Dihedral angles
(at margins)
Face vector 64, 192, 136, 32
Confer
general polytopal classes:
Wythoffian polychora  
analogs:
gocco series  
External
links
hedrondude   polytopewiki   WikiChoron  

As abstract polytope gittith is isomorphic to steth, thereby replacing octagrams by octagons, resp. gocco by socco.


Incidence matrix according to Dynkin symbol

o3o3x4/3x4*b

. . .   .    | 64 |  3  3 |  3  3  3 |  1 1 3
-------------+----+-------+----------+-------
. . x   .    |  2 | 96  * |  2  0  1 |  1 0 2
. . .   x    |  2 |  * 96 |  0  2  1 |  0 1 2
-------------+----+-------+----------+-------
. o3x   .    |  3 |  3  0 | 64  *  * |  1 0 1
. o .   x4*b |  4 |  0  4 |  * 48  * |  0 1 1
. . x4/3x    |  8 |  4  4 |  *  * 24 |  0 0 2
-------------+----+-------+----------+-------
o3o3x   .      4 |  6  0 |  4  0  0 | 16 * *
o3o .   x4*b   8 |  0 12 |  0  6  0 |  * 8 *
. o3x4/3x4*b  24 | 24 24 |  8  6  6 |  * * 8

o3o3/2x4/3x4/3*b

. .   .   .      | 64 |  3  3 |  3  3  3 |  1 1 3
-----------------+----+-------+----------+-------
. .   x   .      |  2 | 96  * |  2  0  1 |  1 0 2
. .   .   x      |  2 |  * 96 |  0  2  1 |  0 1 2
-----------------+----+-------+----------+-------
. o3/2x   .      |  3 |  3  0 | 64  *  * |  1 0 1
. o   .   x4/3*b |  4 |  0  4 |  * 48  * |  0 1 1
. .   x4/3x      |  8 |  4  4 |  *  * 24 |  0 0 2
-----------------+----+-------+----------+-------
o3o3/2x   .        4 |  6  0 |  4  0  0 | 16 * *
o3o   .   x4/3*b   8 |  0 12 |  0  6  0 |  * 8 *
. o3/2x4/3x4/3*b  24 | 24 24 |  8  6  6 |  * * 8

o3/2o3x4/3x4*b

.   . .   .    | 64 |  3  3 |  3  3  3 |  1 1 3
---------------+----+-------+----------+-------
.   . x   .    |  2 | 96  * |  2  0  1 |  1 0 2
.   . .   x    |  2 |  * 96 |  0  2  1 |  0 1 2
---------------+----+-------+----------+-------
.   o3x   .    |  3 |  3  0 | 64  *  * |  1 0 1
.   o .   x4*b |  4 |  0  4 |  * 48  * |  0 1 1
.   . x4/3x    |  8 |  4  4 |  *  * 24 |  0 0 2
---------------+----+-------+----------+-------
o3/2o3x   .      4 |  6  0 |  4  0  0 | 16 * *
o3/2o .   x4*b   8 |  0 12 |  0  6  0 |  * 8 *
.   o3x4/3x4*b  24 | 24 24 |  8  6  6 |  * * 8

o3/2o3/2x4/3x4/3*b

.   .   .   .      | 64 |  3  3 |  3  3  3 |  1 1 3
-------------------+----+-------+----------+-------
.   .   x   .      |  2 | 96  * |  2  0  1 |  1 0 2
.   .   .   x      |  2 |  * 96 |  0  2  1 |  0 1 2
-------------------+----+-------+----------+-------
.   o3/2x   .      |  3 |  3  0 | 64  *  * |  1 0 1
.   o   .   x4/3*b |  4 |  0  4 |  * 48  * |  0 1 1
.   .   x4/3x      |  8 |  4  4 |  *  * 24 |  0 0 2
-------------------+----+-------+----------+-------
o3/2o3/2x   .        4 |  6  0 |  4  0  0 | 16 * *
o3/2o   .   x4/3*b   8 |  0 12 |  0  6  0 |  * 8 *
.   o3/2x4/3x4/3*b  24 | 24 24 |  8  6  6 |  * * 8

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