Acronym	gippid
Name	great prismatodecachoron, omnitruncated pentachoron, Voronoi cell of lattice A4*, permutochoron of 5 elements
	©
Cross sections	©
Circumradius	sqrt(5) = 2.236068
Inradius wrt. hip	sqrt(15)/2 = 1.936492
Inradius wrt. toe	sqrt(5/2) = 1.581139
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o o3o3o . o3o . o o . o3o . o3o3o 1 x3x3x3x x3x3x . toe first x3x . x hip first x . x3x hip first . x3x3x toe first 2 x3x3u . x3u . u u . u3x . u3x3x 3a x3u3x . u3x . H H . x3u . x3u3x 3b x3H . x x . H3x 4a u3x3x . x3x . U U . x3x . x3x3u 4b u3u . u u . u3u 5a x3x3x . opposite toe x3u . H H . u3x . x3x3x opposite toe 5b H3x . x x . x3H 6   u3x . u u . x3u   7 x3x . x opposite hip x . x3x opposite hip (H=hh=x+u, U=uu=u+u)
Lace city in approx. ASCII-art	x3x x3u u3x x3x x3x x3H u3u x3u x3u x3H H3x u3x u3x u3u H3x x3x x3x x3u u3x x3x
Volume	125 sqrt(5)/4 = 69.877124
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: hip toe grip 20 10 )
Dihedral angles	at {4} between hip and hip:   arccos(-2/3) = 131.810315° at {6} between hip and toe:   arccos[-sqrt(3/8)] = 127.761244° at {4} between hip and toe:   arccos[-1/sqrt(6)] = 114.094843° at {6} between toe and toe:   arccos(-1/4) = 104.477512°
Face vector	120, 240, 150, 30
Confer	compounds: afpox   decompositions: deca || gippid   general polytopal classes: Wythoffian polychora   lace simplices   analogs: omnitruncated simplex otSn   omnitruncated Gossetic ot(n2,1)
External links

Note that gippid can be thought of as the external blend of 1 deca + 10 tutatoes + 20 tripufs. This decomposition is described as the degenerate segmentoteron ox3xx3xx3ox&#x.

Incidence matrix according to Dynkin symbol

x3x3x3x

. . . . | 120 |  1  1  1  1 |  1  1  1  1  1  1 | 1  1  1 1
--------+-----+-------------+-------------------+----------
x . . . |   2 | 60  *  *  * |  1  1  1  0  0  0 | 1  1  1 0
. x . . |   2 |  * 60  *  * |  1  0  0  1  1  0 | 1  1  0 1
. . x . |   2 |  *  * 60  * |  0  1  0  1  0  1 | 1  0  1 1
. . . x |   2 |  *  *  * 60 |  0  0  1  0  1  1 | 0  1  1 1
--------+-----+-------------+-------------------+----------
x3x . . |   6 |  3  3  0  0 | 20  *  *  *  *  * | 1  1  0 0
x . x . |   4 |  2  0  2  0 |  * 30  *  *  *  * | 1  0  1 0
x . . x |   4 |  2  0  0  2 |  *  * 30  *  *  * | 0  1  1 0
. x3x . |   6 |  0  3  3  0 |  *  *  * 20  *  * | 1  0  0 1
. x . x |   4 |  0  2  0  2 |  *  *  *  * 30  * | 0  1  0 1
. . x3x |   6 |  0  0  3  3 |  *  *  *  *  * 20 | 0  0  1 1
--------+-----+-------------+-------------------+----------
x3x3x . ♦  24 | 12 12 12  0 |  4  6  0  4  0  0 | 5  *  * *
x3x . x ♦  12 |  6  6  0  6 |  2  0  3  0  3  0 | * 10  * *
x . x3x ♦  12 |  6  0  6  6 |  0  3  3  0  0  2 | *  * 10 *
. x3x3x ♦  24 |  0 12 12 12 |  0  0  0  4  6  4 | *  *  * 5

or
. . . .    | 120 |   2   2 |  2  2  1  1 |  2  2
-----------+-----+---------+-------------+------
x . . .  & |   2 | 120   * |  1  1  1  0 |  1  2
. x . .  & |   2 |   * 120 |  1  1  0  1 |  2  1
-----------+-----+---------+-------------+------
x3x . .  & |   6 |   3   3 | 40  *  *  * |  1  1
x . x .  & |   4 |   2   2 |  * 60  *  * |  1  1
x . . x    |   4 |   4   0 |  *  * 30  * |  0  2
. x3x .    |   6 |   0   6 |  *  *  * 20 |  2  0
-----------+-----+---------+-------------+------
x3x3x .  & ♦  24 |  12  24 |  4  6  0  4 | 10  *
x3x . x  & ♦  12 |  12   6 |  2  3  3  0 |  * 20

snubbed forms: β3x3x3x, x3β3x3x, β3β3x3x, β3x3β3x, β3x3x3β, x3β3β3x, β3β3β3x, β3β3x3β, s3s3s3s

xxxux3xxuxx3xuxxx&#xt   → all heights = sqrt(5/8) = 0.790569
(toe || pseudo (x,x,u)-toe || pseudo (x,u,x)-toe || pseudo (u,x,x)-toe || toe)

o....3o....3o....      & | 48  *  * |  1  1  1  1  0  0  0  0 | 1  1 1  1  1  1 0  0  0 0 | 1 1  1 1
.o...3.o...3.o...      & |  * 48  * |  0  0  0  1  1  1  1  0 | 0  0 0  1  1  1 1  1  1 0 | 0 1  1 2
..o..3..o..3..o..        |  *  * 24 |  0  0  0  0  0  0  2  2 | 0  0 0  0  0  2 0  2  1 1 | 0 0  2 2
-------------------------+----------+-------------------------+---------------------------+---------
x.... ..... .....      & |  2  0  0 | 24  *  *  *  *  *  *  * | 1  1 0  1  0  0 0  0  0 0 | 1 1  1 0
..... x.... .....      & |  2  0  0 |  * 24  *  *  *  *  *  * | 1  0 1  0  1  0 0  0  0 0 | 1 1  0 1
..... ..... x....      & |  2  0  0 |  *  * 24  *  *  *  *  * | 0  1 1  0  0  1 0  0  0 0 | 1 0  1 1
oo...3oo...3oo...&#x   & |  1  1  0 |  *  *  * 48  *  *  *  * | 0  0 0  1  1  1 0  0  0 0 | 0 1  1 1
.x... ..... .....      & |  0  2  0 |  *  *  *  * 24  *  *  * | 0  0 0  1  0  0 1  1  0 0 | 0 1  1 1
..... .x... .....      & |  0  2  0 |  *  *  *  *  * 24  *  * | 0  0 0  0  1  0 1  0  1 0 | 0 1  0 2
.oo..3.oo..3.oo..&#x   & |  0  1  1 |  *  *  *  *  *  * 48  * | 0  0 0  0  0  1 0  1  1 0 | 0 0  1 2
..x.. ..... .....      & |  0  0  2 |  *  *  *  *  *  *  * 24 | 0  0 0  0  0  1 0  1  0 1 | 0 0  2 1
-------------------------+----------+-------------------------+---------------------------+---------
x....3x.... .....      & |  6  0  0 |  3  3  0  0  0  0  0  0 | 8  * *  *  *  * *  *  * * | 1 1  0 0
x.... ..... x....      & |  4  0  0 |  2  0  2  0  0  0  0  0 | * 12 *  *  *  * *  *  * * | 1 0  1 0
..... x....3x....      & |  6  0  0 |  0  3  3  0  0  0  0  0 | *  * 8  *  *  * *  *  * * | 1 0  0 1
xx... ..... .....&#x   & |  2  2  0 |  1  0  0  2  1  0  0  0 | *  * * 24  *  * *  *  * * | 0 1  1 0
..... xx... .....&#x   & |  2  2  0 |  0  1  0  2  0  1  0  0 | *  * *  * 24  * *  *  * * | 0 1  0 1
..... ..... xux..&#xt  & |  2  2  2 |  0  0  1  2  0  0  2  1 | *  * *  *  * 24 *  *  * * | 0 0  1 1
.x...3.x... .....      & |  0  6  0 |  0  0  0  0  3  3  0  0 | *  * *  *  *  * 8  *  * * | 0 1  0 1
.xx.. ..... .....&#x   & |  0  2  2 |  0  0  0  0  1  0  2  1 | *  * *  *  *  * * 24  * * | 0 0  1 1
..... .xux. .....&#xt    |  0  4  2 |  0  0  0  0  0  2  4  0 | *  * *  *  *  * *  * 12 * | 0 0  0 2
..x.. ..... ..x..        |  0  0  4 |  0  0  0  0  0  0  0  4 | *  * *  *  *  * *  *  * 6 | 0 0  2 0
-------------------------+----------+-------------------------+---------------------------+---------
x....3x....3x....      & ♦ 24  0  0 | 12 12 12  0  0  0  0  0 | 4  6 4  0  0  0 0  0  0 0 | 2 *  * *
xx...3xx... .....&#x   & ♦  6  6  0 |  3  3  0  6  3  3  0  0 | 1  0 0  3  3  0 1  0  0 0 | * 8  * *
xxx.. ..... xux..&#xt  & ♦  4  4  4 |  2  0  2  4  2  0  4  4 | 0  1 0  2  0  2 0  2  0 1 | * * 12 *
..... xxux.3xuxx.&#xt  & ♦  6 12  6 |  0  3  3  6  3  6 12  3 | 0  0 1  0  3  3 1  3  3 0 | * *  * 8