Acronym	grico
Name	great rhombated icositetrachoron, cantitruncated icositetrachoron
	©
Cross sections	©
Circumradius	sqrt[10+6 sqrt(2)] = 4.299451
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o4o3o o3o4o . o3o . o o . o3o . o4o3o 1 x3x4x3o x3x4x . girco first x3x . o {6} first x . x3o trip first . x4x3o tic first 2 x3w4o . w3x . x u . w3o . u4x3o 3a u3w4o . w3u . w x . Y3o . x4w3o 3b X . w3x 4a X3x4x . x3X . X w . Y3x . x4w3x 4b Z . x3w 5 x3X4o . X3x . Y V . o3w . u4x3w 6a w3u4x . w3X . w w . Y3w . x4x3Y 6b Z . x3Y 7 w3x4w . u3w . W U . o3x . X4o3w 8a x3x4X . w3Z . x X . w3Y . Z4o3x 8b X3w . Y . w4o3Y 9a w3x4w . x3w . T x . Y3X . Z4o3x 9b V . o3Y . w4o3Y 10 w3u4x . x3V . o u . w3W . X4o3w 11 x3X4o . x3x . S w . W3w . x4x3Y 12a X3x4x . X3Z . x x . x3T . u4x3w 12b Z3w . Y Q . o3x 13 u3w4o . x3w . S X . X3Y . x4w3x 14 x3w4o . u3V . o U . o3Y . x4w3o 15 x3x4x . opposite girco Z3X . w w . T3x . u4x3o 16   V3x . Y Q . o3w . x4x3o opposite tic 17 Z3w . W x . R3R   18a V3u . w Z . X3Y 18b u3w . S 19 x3U . o U . x3Y 20a Z3X . X X . T3x 20b X3w . T 21a U3x . x V . w3Y 21b Q . x3w 22 X3x . S Z . W3w 23 x3X . S u . R3R 24 x3U . x Z . w3W 25a X3Z . X V . Y3w 25b w3X . T Q . w3x 26 U3x . o X . x3T 27a u3V . w U . Y3x 27b w3u . S 28 w3Z . W Z . Y3X 29 x3V . Y x . R3R 30 X3Z . w Q . w3o 31 V3u . o w . x3T 32 w3x . S U . Y3o 33a Z3X . x X . Y3X 33b w3Z . Y 34a x3x . S x . T3x 34b Q . x3o 35 V3x . o w . w3W 36 w3x . T u . W3w 37a Z3w . x x . X3Y 37b w3X . Y V . Y3o 38 w3u . W X . Y3w 39 X3w . w U . x3o 40a x3X . Y w . w3Y 40b Z . Y3x 41 X3x . X V . w3o 42a u3w . w w . x3Y 42b Z . w3x 43a x3w . x x . o3Y 43b X . x3w 44 x3x . o opposite {6} u . o3w 45   x . o3x opposite trip (X=wq=x+w=2x+q, W=2w=2x+2q, Y=x+2q=w+q, Z=3x+q=u+w, V=3x+2q, U=2X=4x+2q, T=2x+3q, S=3w=3x+3q, R=wh, Q=5x+2q)
Lace city in approx. ASCII-art	©   x4x x4u w4x w4x x4u x4x o4w o4X X4x o4X o4w o4w o4Z X4u o4Z o4w x4x x4Z w4X w4X x4Z x4x o4X o4Z W4x o4Z o4X x4u x4Z Y4w Y4w x4Z x4u w4x w4X Y4w Y4w w4X w4x X4x X4u W4x W4x X4u X4x w4x w4X Y4w Y4w w4X w4x x4u x4Z Y4w Y4w x4Z x4u o4X o4Z W4x o4Z o4X x4x x4Z w4X w4X x4Z x4x o4w o4Z X4u o4Z o4w o4w o4X X4x o4X o4w x4x x4u w4x w4x x4u x4x
	(X3x) x3x x3w u3w # x3X w3u w3x x3x x3w X3w w3X w3x u3w Z3w w3Z w3u X3x X3w Z3w V3x x3V w3Z w3X x3X x3X Z3X X3Z X3x w3u w3X Z3X V3u u3V X3Z X3w u3w w3x w3Z X3Z U3x x3U Z3X Z3w x3w x3x x3V u3V x3U U3x V3u V3x x3x w3x w3Z X3Z U3x x3U Z3X Z3w x3w w3u w3X Z3X V3u u3V X3Z X3w u3w x3X Z3X X3Z X3x X3x X3w Z3w V3x x3V w3Z w3X x3X u3w Z3w w3Z w3u x3w X3w w3X w3x x3x x3w u3w # x3X w3u w3x x3x (X3x)
	©   o3x o3w x3w w3x w3o x3o o3x o3Y x3Y Y3x Y3o x3o o3w o3Y w3Y Y3w Y3o w3o (W3w) x3w x3Y X3Y # w3W Y3X Y3x w3x w3x w3Y X3Y T3x x3T Y3X Y3w x3w Y3x Y3w W3w T3x x3T w3W w3Y x3Y w3o w3W R3R W3w o3w x3o Y3o Y3X x3T R3R R3R T3x X3Y o3Y o3x x3o Y3o Y3X x3T R3R R3R T3x X3Y o3Y o3x w3o w3W R3R W3w o3w Y3x Y3w W3w T3x x3T w3W w3Y x3Y w3x w3Y X3Y T3x x3T Y3X Y3w x3w x3w x3Y X3Y # w3W Y3X Y3x w3x (W3w) o3w o3Y w3Y Y3w Y3o w3o o3x o3Y x3Y Y3x Y3o x3o o3x o3w x3w w3x w3o x3o
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: girco tic trip grico 24 24 96 )
Dihedral angles	at {3} between tic and trip:   150° at {4} between girco and trip:   arccos[-sqrt(2/3)] = 144.735610° at {8} between girco and tic:   135° at {6} between girco and girco:   120°
Face vector	576, 1152, 720, 144
Confer	Grünbaumian relatives: 2grico   general polytopal classes: Wythoffian polychora   partial Stott expansions
External links

As abstract polytope grico is isomorphic to gaqri, thereby replacing the octagons by octagrams, resp. replacing girco by quitco and tic by quith.

Note that grico can be thought of as the external blend of 1 prico + 24 sircoatics + 96 opes + 96 thiddips + 24 toagircoes. This decomposition is described as the degenerate segmentoteron xo3ox4xx3xx&#x.

Incidence matrix according to Dynkin symbol

x3x4x3o

. . . . | 576 |   1   1   2 |  1   2   2   1 |  2  1  1
--------+-----+-------------+----------------+---------
x . . . |   2 | 288   *   * |  1   2   0   0 |  2  1  0
. x . . |   2 |   * 288   * |  1   0   2   0 |  2  0  1
. . x . |   2 |   *   * 576 |  0   1   1   1 |  1  1  1
--------+-----+-------------+----------------+---------
x3x . . |   6 |   3   3   0 | 96   *   *   * |  2  0  0
x . x . |   4 |   2   0   2 |  * 288   *   * |  1  1  0
. x4x . |   8 |   0   4   4 |  *   * 144   * |  1  0  1
. . x3o |   3 |   0   0   3 |  *   *   * 192 |  0  1  1
--------+-----+-------------+----------------+---------
x3x4x . ♦  48 |  24  24  24 |  8  12   6   0 | 24  *  *
x . x3o ♦   6 |   3   0   6 |  0   3   0   2 |  * 96  *
. x4x3o ♦  24 |   0  12  24 |  0   0   6   8 |  *  * 24

snubbed forms: β3x4x3o, x3β4x3o, x3x4β3o, s3s4x3o, β3x4β3o, x3β4β3o, β3β4β3o

x3x4x3/2o

. . .   . | 576 |   1   1   2 |  1   2   2   1 |  2  1  1
----------+-----+-------------+----------------+---------
x . .   . |   2 | 288   *   * |  1   2   0   0 |  2  1  0
. x .   . |   2 |   * 288   * |  1   0   2   0 |  2  0  1
. . x   . |   2 |   *   * 576 |  0   1   1   1 |  1  1  1
----------+-----+-------------+----------------+---------
x3x .   . |   6 |   3   3   0 | 96   *   *   * |  2  0  0
x . x   . |   4 |   2   0   2 |  * 288   *   * |  1  1  0
. x4x   . |   8 |   0   4   4 |  *   * 144   * |  1  0  1
. . x3/2o |   3 |   0   0   3 |  *   *   * 192 |  0  1  1
----------+-----+-------------+----------------+---------
x3x4x   . ♦  48 |  24  24  24 |  8  12   6   0 | 24  *  *
x . x3/2o ♦   6 |   3   0   6 |  0   3   0   2 |  * 96  *
. x4x3/2o ♦  24 |   0  12  24 |  0   0   6   8 |  *  * 24

wx3xx3xw4xo&#zx   → height = 0
(tegum sum of (w,x,x,x)-gidpith and (x,x,w)-tico)

o.3o.3o.4o.     | 384   * |   1   1   1   1  0  0 |  1  1  1  1   1   1  0 | 1  1  1  1
.o3.o3.o4.o     |   * 192 |   0   0   0   2  1  1 |  0  0  0  2   2   1  1 | 0  2  1  1
----------------+---------+-----------------------+------------------------+-----------
.. x. .. ..     |   2   0 | 192   *   *   *  *  * |  1  1  0  0   1   0  0 | 1  1  0  1
.. .. x. ..     |   2   0 |   * 192   *   *  *  * |  1  0  1  1   0   0  0 | 1  1  1  0
.. .. .. x.     |   2   0 |   *   * 192   *  *  * |  0  1  1  0   0   1  0 | 1  0  1  1
oo3oo3oo4oo&#x  |   1   1 |   *   *   * 384  *  * |  0  0  0  1   1   1  0 | 0  1  1  1
.x .. .. ..     |   0   2 |   *   *   *   * 96  * |  0  0  0  2   0   0  1 | 0  2  1  0
.. .x .. ..     |   0   2 |   *   *   *   *  * 96 |  0  0  0  0   2   0  1 | 0  2  0  1
----------------+---------+-----------------------+------------------------+-----------
.. x.3x. ..     |   6   0 |   3   3   0   0  0  0 | 64  *  *  *   *   *  * | 1  1  0  0
.. x. .. x.     |   4   0 |   2   0   2   0  0  0 |  * 96  *  *   *   *  * | 1  0  0  1
.. .. x.4x.     |   8   0 |   0   4   4   0  0  0 |  *  * 48  *   *   *  * | 1  0  1  0
wx .. xw ..&#zx |   4   4 |   0   2   0   4  2  0 |  *  *  * 96   *   *  * | 0  1  1  0
.. xx .. ..&#x  |   2   2 |   1   0   0   2  0  1 |  *  *  *  * 192   *  * | 0  1  0  1
.. .. .. xo&#x  |   2   1 |   0   0   1   2  0  0 |  *  *  *  *   * 192  * | 0  0  1  1
.x3.x .. ..     |   0   6 |   0   0   0   0  3  3 |  *  *  *  *   *   * 32 | 0  2  0  0
----------------+---------+-----------------------+------------------------+-----------
.. x.3x.4x.     ♦  48   0 |  24  24  24   0  0  0 |  8 12  6  0   0   0  0 | 8  *  *  *
wx3xx3xw ..&#zx ♦  24  24 |  12  12   0  24 12 12 |  4  0  0  6  12   0  4 | * 16  *  *
wx .. xw4xo&#zx ♦  16   8 |   0   8   8  16  4  0 |  0  0  2  4   0   8  0 | *  * 24  *
.. xx .. xo&#x  ♦   4   2 |   2   0   2   4  0  1 |  0  1  0  0   2   2  0 | *  *  * 96

xwX3ooo3wxx4xux&#zxt   → height = 0, X=Q+x=w+q = 3.828427

o..3o..3o..4o..      | 192   *   * |   2  1   1   0   0   0  0 |  1  2  2  1  0   0  0  0 |  1  1  2  0 0
.o.3.o.3.o.4.o.      |   * 192   * |   0  0   1   2   1   0  0 |  0  0  2  1  1   2  0  0 |  0  1  2  1 0
..o3..o3..o4..o      |   *   * 192 |   0  0   0   0   1   2  1 |  0  0  0  1  0   2  1  2 |  0  0  2  1 1
---------------------+-------------+---------------------------+--------------------------+--------------
x.. ... ... ...      |   2   0   0 | 192  *   *   *   *   *  * |  1  1  1  0  0   0  0  0 |  1  1  1  0 0
... ... ... x..      |   2   0   0 |   * 96   *   *   *   *  * |  0  2  0  1  0   0  0  0 |  1  0  2  0 0
oo.3oo.3oo.4oo.&#x   |   1   1   0 |   *  * 192   *   *   *  * |  0  0  2  1  0   0  0  0 |  0  1  2  0 0
... ... .x. ...      |   0   2   0 |   *  *   * 192   *   *  * |  0  0  1  0  1   1  0  0 |  0  1  1  1 0
.oo3.oo3.oo4.oo&#x   |   0   1   1 |   *  *   *   * 192   *  * |  0  0  0  1  0   2  0  0 |  0  0  2  1 0
... ... ..x ...      |   0   0   2 |   *  *   *   *   * 192  * |  0  0  0  0  0   1  1  1 |  0  0  1  1 1
... ... ... ..x      |   0   0   2 |   *  *   *   *   *   * 96 |  0  0  0  1  0   0  0  2 |  0  0  2  0 1
---------------------+-------------+---------------------------+--------------------------+--------------
x..3o.. ... ...      |   3   0   0 |   3  0   0   0   0   0  0 | 64  *  *  *  *   *  *  * |  1  1  0  0 0
x.. ... ... x..      |   4   0   0 |   2  2   0   0   0   0  0 |  * 96  *  *  *   *  *  * |  1  0  1  0 0
xw. ... wx. ...&#zx  |   4   4   0 |   2  0   4   2   0   0  0 |  *  * 96  *  *   *  *  * |  0  1  1  0 0
... ... ... xux&#xt  |   2   2   2 |   0  1   2   0   2   0  1 |  *  *  * 96  *   *  *  * |  0  0  2  0 0
... .o.3.x. ...      |   0   3   0 |   0  0   0   3   0   0  0 |  *  *  *  * 64   *  *  * |  0  1  0  1 0
... ... .xx ...&#x   |   0   2   2 |   0  0   0   1   2   1  0 |  *  *  *  *  * 192  *  * |  0  0  1  1 0
... ..o3..x ...      |   0   0   3 |   0  0   0   0   0   3  0 |  *  *  *  *  *   * 64  * |  0  0  0  1 1
... ... ..x4..x      |   0   0   8 |   0  0   0   0   0   4  4 |  *  *  *  *  *   *  * 48 |  0  0  1  0 1
---------------------+-------------+---------------------------+--------------------------+--------------
x..3o.. ... x..      ♦   6   0   0 |   6  3   0   0   0   0  0 |  2  3  0  0  0   0  0  0 | 32  *  *  * *
xw.3oo.3wx. ...&#zx  ♦  12  12   0 |  12  0  12  12   0   0  0 |  4  0  6  0  4   0  0  0 |  * 16  *  * *
xwX ... wxx4xux&#zxt ♦  16  16  16 |   8  8  16   8  16   8  8 |  0  4  4  8  0   8  0  2 |  *  * 24  * *
... .oo3.xx ...&#x   ♦   0   3   3 |   0  0   0   3   3   3  0 |  0  0  0  0  1   3  1  0 |  *  *  * 64 *
... ..o3..x4..x      ♦   0   0  24 |   0  0   0   0   0  24 12 |  0  0  0  0  0   0  8  6 |  *  *  *  * 8