Acronym	gidpith
Name	great disprismatotesseractihexadecachoron, great prismated tesseract, omnitruncated tesseract
Cross sections	©
Circumradius	sqrt[8+3 sqrt(2)] = 3.498949
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o4o o3o3o . o3o . o o . o4o . o3o4o 1 x3x3x4x x3x3x . toe first x3x . x hip first x . x4x op first . x3x4x girco first 2 x3x3w . x3u . w u . u4x . u3x4x 3a x3u3w . u3x . C x . X4x . x3u4x 3b Y . x4w 4 x3X3x . x3X . w u . u4w . x3x4w 5 u3x3X . x3x . D Z . x4w . x3x4w 6a u3w3u . x3Z . x x . x4w . x3u4x 6b u3w . C 7a x3x3Z . x3w . D X . u4w . u3x4x 7b A . u4x 8a x3w3Y . u3Z . x w . x4w . x3x4x opposite girco 8b Y3w3x . Y3w . C Z . X4x 8c B . x4x 9a Z3x3x . Y3X . w w . x4w   9b u3w . D Z . X4x 9c B . x4x 10a u3w3u . Z3x . C X . u4w 10b A . u4x 11 X3x3u . x3A . x x . x4w 12a x3X3x . Z3u . w Z . x4w 12b X3x . D 13a w3u3x . u3Z . w u . u4w 13b x3X . D 14a w3x3x . A3x . x x . X4x 14b Y . x4w 15 x3x3x . opposite toe x3Z . C u . u4x 16a   X3Y . w x . x4x opposite op 16b w3u . D 17a Z3u . x   17b w3Y . C 18 w3x . D 19a Z3x . x 19b w3u . C 20 x3x . D 21 X3x . w 22 x3u . C 23 u3x . w 24 x3x . x opposite hip (X=2x+q=x+w, Y=3x, Z=3x+q=u+w, A=4x+q, B=5x+q, C=x+2q, D=x+3q)
Lace city in approx. ASCII-art	©   x4x u4x x4w x4w u4x x4x x4x X4x u4w u4w X4x x4x u4x X4x x4w x4w X4x u4x x4w u4w x4w x4w u4w x4w x4w u4w x4w x4w u4w x4w u4x X4x x4w x4w X4x u4x x4x X4x u4w u4w X4x x4x x4x u4x x4w x4w u4x x4x
	x3x x3x x3u x3u u3x u3x x3X x3X x3x x3x u3w x3Z x3Z u3w x3w x3w Y3w u3Z u3Z Y3w u3w Y3X Y3X u3w Z3x Z3x x3A x3A X3x Z3u Z3u X3x x3X u3Z u3Z x3X A3x A3x x3Z x3Z w3u X3Y X3Y w3u w3Y Z3u Z3u w3Y w3x w3x w3u Z3x Z3x w3u x3x x3x X3x X3x 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 8 32 24 16 )
Confer	segmentochora: toe || girco   related CRFs: prico
External links

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 the girco would lead to the prico (which would have an even larger symmetry)!

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

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