Acronym gippid
Name great prismatodecachoron,
Voronoi cell of lattice A4*
 
 ©
Cross sections
 ©
Circumradius sqrt(5) = 2.236068
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o3o o3o3o . o3o . o o . o3o . o3o3o
1x3x3x3x 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     
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: hip toe
grip 2010
)
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(-sqrt[1/6]) = 114.094843°
  • at {6} between toe and toe:   arccos(-1/4) = 104.477512°
Confer
compounds:
afpox  
decompositions:
deca || gippid  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

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

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