Acronym gidpith
Name great disprismatotesseractihexadecachoron,
great prismated tesseract,
omnitruncated tesseract
 
Cross sections
 ©
Circumradius sqrt[8+3 sqrt(2)] = 3.498949
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1x3x3x4x x3x3x .
toe first
x3x . x
hip first
x . x4x
op first
. x3x4x
girco first
2 x3x3w . x3u . w u . u4x . u3x4x
3a x3u3w . u3x . X x . U4x . x3u4x
3b D . x4w
4 x3U3x . x3U . w u . u4w . x3x4w
5 u3x3U . x3x . A W . x4w . x3x4w
6a u3w3u . x3W . x x . x4w . x3u4x
6b u3w . X
7a x3x3W . x3w . A U . u4w . u3x4x
7b Y . u4x
8a x3w3D . u3W . x w . x4w . x3x4x
opposite girco
8b D3w3x . D3w . X W . U4x
8c B . x4x
9a W3x3x . D3U . w w . x4w  
9b u3w . A W . U4x
9c B . x4x
10a u3w3u . W3x . X U . u4w
10b Y . u4x
11 U3x3u . x3Y . x x . x4w
12a x3U3x . W3u . w W . x4w
12b U3x . A
13a w3u3x . u3W . w u . u4w
13b x3U . A
14a w3x3x . Y3x . x x . U4x
14b D . x4w
15 x3x3x .
opposite toe
x3W . X u . u4x
16a   U3D . w x . x4x
opposite op
16b w3u . A
17a W3u . x  
17b w3D . X
18 w3x . A
19a W3x . x
19b w3u . X
20 x3x . A
21 U3x . w
22 x3u . X
23 u3x . w
24 x3x . x
opposite hip
(D=3x, U=2x+q=x+w, W=3x+q=u+w, X=x+2q, Y=4x+q, A=x+3q, B=5x+q)
Lace city
in approx. ASCII-art
 ©  
    x4x u4x x4w   x4w u4x x4x    
                                 
x4x     D4x u4w   u4w D4x     x4x
                                 
u4x D4x     x4X   x4X     D4x u4x
                                 
x4w u4w x4X           x4X u4w x4w
                                 
                                 
x4w u4w x4X           x4X u4w x4w
                                 
u4x D4x     x4X   x4X     D4x u4x
                                 
x4x     D4x u4w   u4w D4x     x4x
                                 
    x4x u4x x4w   x4w u4x x4x    
                        x3x         x3x                        
                                                               
                x3u                         x3u                
                                                               
        u3x                                         u3x        
                x3U                         x3U                
x3x                                                         x3x
        u3w             x3W         x3W             u3w        
                                                               
x3w                                                         x3w
                                                               
        D3w             u3W         u3W             D3w        
                                                               
u3w             D3U                         D3U             u3w
        W3x                                         W3x        
                        x3Y         x3Y                        
U3x             W3u                         W3u             U3x
x3U             u3W                         u3W             x3U
                        Y3x         Y3x                        
        x3W                                         x3W        
w3u             U3D                         U3D             w3u
                                                               
        w3D             W3u         W3u             w3D        
                                                               
w3x                                                         w3x
                                                               
        w3u             W3x         W3x             w3u        
x3x                                                         x3x
                U3x                         U3x                
        x3u                                         x3u        
                                                               
                u3x                         u3x                
                                                               
                        x3x         x3x                        
Coordinates ((1+3 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: girco hip op toe
gidpith 8322416
)
Dihedral angles
  • at {6} between hip and toe:   150°
  • at {4} between hip and op:   arccos(-sqrt[2/3]) = 144.735610°
  • at {4} between op and toe:   135°
  • at {8} between girco and op:   135°
  • at {4} between girco and hip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {6} between girco and toe:   120°
Confer
segmentochora:
toe || girco  
related CRFs:
prico  
decompositions:
proh || gidpith   tico || gidpith  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope gidpith is isomorphic to gaquidpoth, thereby replacing the octagons by octagrams, resp. replacing the girco by quitco and the op by stop.

Augmenting toe || girco onto each girco of gidpith would lead to prico (which then would have an even larger symmetry)!

Note that gidpith can be thought of as the external blend of 1 tico + 16 topes + 32 thiddips + 24 squacupes + 8 toagircos. This decomposition is described as the degenerate segmentoteron xx3xx3xx4ox&#x. – Alternatively it also can be decomposed into 1 proh + 16 coatoes + 32 tricupes + 24 sodips + 8 ticagircos according to xx3ox3xx4xx&#x.


Incidence matrix according to Dynkin symbol

x3x3x4x

. . . . | 384 |   1   1   1   1 |  1  1  1  1  1  1 |  1  1  1 1
--------+-----+-----------------+-------------------+-----------
x . . . |   2 | 192   *   *   * |  1  1  1  0  0  0 |  1  1  1 0
. x . . |   2 |   * 192   *   * |  1  0  0  1  1  0 |  1  1  0 1
. . x . |   2 |   *   * 192   * |  0  1  0  1  0  1 |  1  0  1 1
. . . x |   2 |   *   *   * 192 |  0  0  1  0  1  1 |  0  1  1 1
--------+-----+-----------------+-------------------+-----------
x3x . . |   6 |   3   3   0   0 | 64  *  *  *  *  * |  1  1  0 0
x . x . |   4 |   2   0   2   0 |  * 96  *  *  *  * |  1  0  1 0
x . . x |   4 |   2   0   0   2 |  *  * 96  *  *  * |  0  1  1 0
. x3x . |   6 |   0   3   3   0 |  *  *  * 64  *  * |  1  0  0 1
. x . x |   4 |   0   2   0   2 |  *  *  *  * 96  * |  0  1  0 1
. . x4x |   8 |   0   0   4   4 |  *  *  *  *  * 48 |  0  0  1 1
--------+-----+-----------------+-------------------+-----------
x3x3x .   24 |  12  12  12   0 |  4  6  0  4  0  0 | 16  *  * *
x3x . x   12 |   6   6   0   6 |  2  0  3  0  3  0 |  * 32  * *
x . x4x   16 |   8   0   8   8 |  0  4  4  0  0  2 |  *  * 24 *
. x3x4x   48 |   0  24  24  24 |  0  0  0  8 12  6 |  *  *  * 8

snubbed forms: β3x3x4x, x3β3x4x, x3x3β4x, x3x3x4s, β3β3x4x, β3x3β4x, β3x3x4β, x3β3β4x, x3β3x4β, x3x3β4β, s3s3s4x, β3β3x4β, β3x3β4β, x3β3β4β, s3s3s4s


xuxxxxux3xxuxxuxx4xxxwwxxx&#xt   → all non-central heights = 1/sqrt(2) = 0.707107
                                   central height = 1
(girco || pseudo (u,x,x)-girco || pseudo (x,u,x)-girco || pseudo (x,x,w)-girco || pseudo (x,x,w)-girco || pseudo (x,u,x)-girco || pseudo (u,x,x)-girco || girco)

o.......3o.......4o.......      & | 96  *  *  * |  1  1  1  1  0  0  0  0  0  0  0  0  0 |  1  1  1  1  1  1  0  0  0  0  0  0  0  0  0 | 1  1  1  1 0  0 0
.o......3.o......4.o......      & |  * 96  *  * |  0  0  0  1  1  1  1  0  0  0  0  0  0 |  0  0  0  1  1  1  1  1  1  0  0  0  0  0  0 | 0  1  1  1 1  0 0
..o.....3..o.....4..o.....      & |  *  * 96  * |  0  0  0  0  0  0  1  1  1  1  0  0  0 |  0  0  0  1  0  0  0  1  1  1  1  1  0  0  0 | 0  1  1  0 1  1 0
...o....3...o....4...o....      & |  *  *  * 96 |  0  0  0  0  0  0  0  0  0  1  1  1  1 |  0  0  0  0  0  0  0  1  0  0  1  1  1  1  1 | 0  1  0  0 1  1 1
----------------------------------+-------------+----------------------------------------+----------------------------------------------+------------------
x....... ........ ........      & |  2  0  0  0 | 48  *  *  *  *  *  *  *  *  *  *  *  * |  1  1  0  1  0  0  0  0  0  0  0  0  0  0  0 | 1  1  1  0 0  0 0
........ x....... ........      & |  2  0  0  0 |  * 48  *  *  *  *  *  *  *  *  *  *  * |  1  0  1  0  1  0  0  0  0  0  0  0  0  0  0 | 1  1  0  1 0  0 0
........ ........ x.......      & |  2  0  0  0 |  *  * 48  *  *  *  *  *  *  *  *  *  * |  0  1  1  0  0  1  0  0  0  0  0  0  0  0  0 | 1  0  1  1 0  0 0
oo......3oo......4oo......&#x   & |  1  1  0  0 |  *  *  * 96  *  *  *  *  *  *  *  *  * |  0  0  0  1  1  1  0  0  0  0  0  0  0  0  0 | 0  1  1  1 0  0 0
........ .x...... ........      & |  0  2  0  0 |  *  *  *  * 48  *  *  *  *  *  *  *  * |  0  0  0  0  1  0  1  1  0  0  0  0  0  0  0 | 0  1  0  1 1  1 0
........ ........ .x......      & |  0  2  0  0 |  *  *  *  *  * 48  *  *  *  *  *  *  * |  0  0  0  0  0  1  1  0  1  0  0  0  0  0  0 | 0  0  1  1 1  1 0
.oo.....3.oo.....4.oo.....&#x   & |  0  1  1  0 |  *  *  *  *  *  * 96  *  *  *  *  *  * |  0  0  0  1  0  0  0  1  1  0  0  0  0  0  0 | 0  1  1  0 1  1 0
..x..... ........ ........      & |  0  0  2  0 |  *  *  *  *  *  *  * 48  *  *  *  *  * |  0  0  0  1  0  0  0  0  0  1  1  0  0  0  0 | 0  1  1  0 0  1 0
........ ........ ..x.....      & |  0  0  2  0 |  *  *  *  *  *  *  *  * 48  *  *  *  * |  0  0  0  0  0  0  0  0  1  1  0  1  0  0  0 | 0  0  1  0 1  1 0
..oo....3..oo....4..oo....&#x   & |  0  0  1  1 |  *  *  *  *  *  *  *  *  * 96  *  *  * |  0  0  0  0  0  0  0  1  0  0  1  1  0  0  0 | 0  1  0  0 1  1 0
...x.... ........ ........      & |  0  0  0  2 |  *  *  *  *  *  *  *  *  *  * 48  *  * |  0  0  0  0  0  0  0  0  0  0  1  0  1  1  0 | 0  1  0  0 0  1 1
........ ...x.... ........      & |  0  0  0  2 |  *  *  *  *  *  *  *  *  *  *  * 48  * |  0  0  0  0  0  0  0  1  0  0  0  0  1  0  1 | 0  1  0  0 1  0 1
...oo...3...oo...4...oo...&#x     |  0  0  0  2 |  *  *  *  *  *  *  *  *  *  *  *  * 48 |  0  0  0  0  0  0  0  0  0  0  0  1  0  1  1 | 0  0  0  0 1  1 1
----------------------------------+-------------+----------------------------------------+----------------------------------------------+------------------
x.......3x....... ........      & |  6  0  0  0 |  3  3  0  0  0  0  0  0  0  0  0  0  0 | 16  *  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  1  0  0 0  0 0
x....... ........ x.......      & |  4  0  0  0 |  2  0  2  0  0  0  0  0  0  0  0  0  0 |  * 24  *  *  *  *  *  *  *  *  *  *  *  *  * | 1  0  1  0 0  0 0
........ x.......4x.......      & |  8  0  0  0 |  0  4  4  0  0  0  0  0  0  0  0  0  0 |  *  * 12  *  *  *  *  *  *  *  *  *  *  *  * | 1  0  0  1 0  0 0
xux..... ........ ........&#xt  & |  2  2  2  0 |  1  0  0  2  0  0  2  1  0  0  0  0  0 |  *  *  * 48  *  *  *  *  *  *  *  *  *  *  * | 0  1  1  0 0  0 0
........ xx...... ........&#x   & |  2  2  0  0 |  0  1  0  2  1  0  0  0  0  0  0  0  0 |  *  *  *  * 48  *  *  *  *  *  *  *  *  *  * | 0  1  0  1 0  0 0
........ ........ xx......&#x   & |  2  2  0  0 |  0  0  1  2  0  1  0  0  0  0  0  0  0 |  *  *  *  *  * 48  *  *  *  *  *  *  *  *  * | 0  0  1  1 0  0 0
........ .x......4.x......      & |  0  8  0  0 |  0  0  0  0  4  4  0  0  0  0  0  0  0 |  *  *  *  *  *  * 12  *  *  *  *  *  *  *  * | 0  0  0  1 1  0 0
........ .xux.... ........&#xt  & |  0  2  2  2 |  0  0  0  0  1  0  2  0  0  2  0  1  0 |  *  *  *  *  *  *  * 48  *  *  *  *  *  *  * | 0  1  0  0 1  0 0
........ ........ .xx.....&#x   & |  0  2  2  0 |  0  0  0  0  0  1  2  0  1  0  0  0  0 |  *  *  *  *  *  *  *  * 48  *  *  *  *  *  * | 0  0  1  0 1  0 0
..x..... ........ ..x.....      & |  0  0  4  0 |  0  0  0  0  0  0  0  2  2  0  0  0  0 |  *  *  *  *  *  *  *  *  * 24  *  *  *  *  * | 0  0  1  0 0  1 0
..xx.... ........ ........&#x   & |  0  0  2  2 |  0  0  0  0  0  0  0  1  0  2  1  0  0 |  *  *  *  *  *  *  *  *  *  * 48  *  *  *  * | 0  1  0  0 0  1 0
........ ........ ..xwwx..&#xt    |  0  0  4  4 |  0  0  0  0  0  0  0  0  2  4  0  0  2 |  *  *  *  *  *  *  *  *  *  *  * 24  *  *  * | 0  0  0  0 1  1 0
...x....3...x.... ........      & |  0  0  0  6 |  0  0  0  0  0  0  0  0  0  0  3  3  0 |  *  *  *  *  *  *  *  *  *  *  *  * 16  *  * | 0  1  0  0 0  0 1
...xx... ........ ........&#x     |  0  0  0  4 |  0  0  0  0  0  0  0  0  0  0  2  0  2 |  *  *  *  *  *  *  *  *  *  *  *  *  * 24  * | 0  0  0  0 0  1 1
........ ...xx... ........&#x     |  0  0  0  4 |  0  0  0  0  0  0  0  0  0  0  0  2  2 |  *  *  *  *  *  *  *  *  *  *  *  *  *  * 24 | 0  0  0  0 1  0 1
----------------------------------+-------------+----------------------------------------+----------------------------------------------+------------------
x.......3x.......4x.......      &  48  0  0  0 | 24 24 24  0  0  0  0  0  0  0  0  0  0 |  8 12  6  0  0  0  0  0  0  0  0  0  0  0  0 | 2  *  *  * *  * *
xuxx....3xxux.... ........&#xt  &   6  6  6  6 |  3  3  0  6  3  0  6  3  0  6  3  3  0 |  1  0  0  3  3  0  0  3  0  0  3  0  1  0  0 | * 16  *  * *  * *
xux..... ........ xxx.....&#xt  &   4  4  4  0 |  2  0  2  4  0  2  4  2  2  0  0  0  0 |  0  1  0  2  0  2  0  0  2  1  0  0  0  0  0 | *  * 24  * *  * *
........ xx......4xx......&#x   &   8  8  0  0 |  0  4  4  8  4  4  0  0  0  0  0  0  0 |  0  0  1  0  4  4  1  0  0  0  0  0  0  0  0 | *  *  * 12 *  * *
........ .xuxxux.4.xxwwxx.&#xt      0 16 16 16 |  0  0  0  0  8  8 16  0  8 16  0  8  8 |  0  0  0  0  0  0  2  8  8  0  0  4  0  0  4 | *  *  *  * 6  * *
..xxxx.. ........ ..xwwx..&#xt      0  0  8  8 |  0  0  0  0  4  4  8  4  4  8  4  0  4 |  0  0  0  0  0  0  0  0  0  2  4  2  0  2  0 | *  *  *  * * 12 *
...xx...3...xx... ........&#x       0  0  0 12 |  0  0  0  0  0  0  0  0  0  0  6  6  6 |  0  0  0  0  0  0  0  0  0  0  0  0  2  3  3 | *  *  *  * *  * 8

wx3xx3xw *b3xx&#zx   → height = 0
(tegum sum of 2 mutually gyrated (w,x,x,x)-ticoes)

o.3o.3o. *b3o.     | 192   * |  1  1  1   1  0  0  0 |  1  1  1  1  1  1  0  0  0 | 1 1  1  1 0
.o3.o3.o *b3.o     |   * 192 |  0  0  0   1  1  1  1 |  0  0  0  1  1  1  1  1  1 | 0 1  1  1 1
-------------------+---------+-----------------------+----------------------------+------------
.. x. ..    ..     |   2   0 | 96  *  *   *  *  *  * |  1  1  0  0  1  0  0  0  0 | 1 1  0  1 0
.. .. x.    ..     |   2   0 |  * 96  *   *  *  *  * |  1  0  1  1  0  0  0  0  0 | 1 1  1  0 0
.. .. ..    x.     |   2   0 |  *  * 96   *  *  *  * |  0  1  1  0  0  1  0  0  0 | 1 0  1  1 0
oo3oo3oo *b3oo&#x  |   1   1 |  *  *  * 192  *  *  * |  0  0  0  1  1  1  0  0  0 | 0 1  1  1 0
.x .. ..    ..     |   0   2 |  *  *  *   * 96  *  * |  0  0  0  1  0  0  1  1  0 | 0 1  1  0 1
.. .x ..    ..     |   0   2 |  *  *  *   *  * 96  * |  0  0  0  0  1  0  1  0  1 | 0 1  0  1 1
.. .. ..    .x     |   0   2 |  *  *  *   *  *  * 96 |  0  0  0  0  0  1  0  1  1 | 0 0  1  1 1
-------------------+---------+-----------------------+----------------------------+------------
.. x.3x.    ..     |   6   0 |  3  3  0   0  0  0  0 | 32  *  *  *  *  *  *  *  * | 1 1  0  0 0
.. x. .. *b3x.     |   6   0 |  3  0  3   0  0  0  0 |  * 32  *  *  *  *  *  *  * | 1 0  0  1 0
.. .. x.    x.     |   4   0 |  0  2  2   0  0  0  0 |  *  * 48  *  *  *  *  *  * | 1 0  1  0 0
wx .. xw    ..&#zx |   4   4 |  0  2  0   4  2  0  0 |  *  *  * 48  *  *  *  *  * | 0 1  1  0 0
.. xx ..    ..&#x  |   2   2 |  1  0  0   2  0  1  0 |  *  *  *  * 96  *  *  *  * | 0 1  0  1 0
.. .. ..    xx&#x  |   2   2 |  0  0  1   2  0  0  1 |  *  *  *  *  * 96  *  *  * | 0 0  1  1 0
.x3.x ..    ..     |   0   6 |  0  0  0   0  3  3  0 |  *  *  *  *  *  * 32  *  * | 0 1  0  0 1
.x .. ..    .x     |   0   4 |  0  0  0   0  2  0  2 |  *  *  *  *  *  *  * 48  * | 0 0  1  0 1
.. .x .. *b3.x     |   0   6 |  0  0  0   0  0  3  3 |  *  *  *  *  *  *  *  * 32 | 0 0  0  1 1
-------------------+---------+-----------------------+----------------------------+------------
.. x.3x. *b3x.       24   0 | 12 12 12   0  0  0  0 |  4  4  6  0  0  0  0  0  0 | 8 *  *  * *
wx3xx3xw    ..&#zx   24  24 | 12 12  0  24 12 12  0 |  4  0  0  6 12  0  4  0  0 | * 8  *  * *
wx .. xw    xx&#zx    8   8 |  0  4  4   8  4  0  4 |  0  0  2  2  0  4  0  2  0 | * * 24  * *
.. xx .. *b3xx&#x     6   6 |  3  0  3   6  0  3  3 |  0  1  0  0  3  3  0  0  1 | * *  * 32 *
.x3.x .. *b3.x        0  24 |  0  0  0   0 12 12 12 |  0  0  0  0  0  0  4  6  4 | * *  *  * 8

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