Acronym griddip, K-4.150
Name great-rhombicosidodecahedron prism
Segmentochoron display
Cross sections
 ©
Circumradius sqrt[8+3 sqrt(5)] = 3.835128
Dihedral angles
  • at {4} between cube and hip:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • at {4} between cube and dip:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
  • at {4} between dip and hip:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • at {4} between cube and grid:   90°
  • at {10} between dip and grid:   90°
  • at {6} between grid and hip:   90°
Confer
general polytopal classes:
segmentochora  
External
links
hedrondude   wikipedia   polytopewiki  

As abstract polytope griddip is isomorphic to gaquatiddip, thereby replacing decagons by decagrams, resp. replacing grid by gaquatid and dip by stiddip.


Incidence matrix according to Dynkin symbol

x x3x5x

. . . . | 240 |   1   1   1   1 |  1  1  1  1  1  1 |  1  1  1 1
--------+-----+-----------------+-------------------+-----------
x . . . |   2 | 120   *   *   * |  1  1  1  0  0  0 |  1  1  1 0
. x . . |   2 |   * 120   *   * |  1  0  0  1  1  0 |  1  1  0 1
. . x . |   2 |   *   * 120   * |  0  1  0  1  0  1 |  1  0  1 1
. . . x |   2 |   *   *   * 120 |  0  0  1  0  1  1 |  0  1  1 1
--------+-----+-----------------+-------------------+-----------
x x . . |   4 |   2   2   0   0 | 60  *  *  *  *  * |  1  1  0 0
x . x . |   4 |   2   0   2   0 |  * 60  *  *  *  * |  1  0  1 0
x . . x |   4 |   2   0   0   2 |  *  * 60  *  *  * |  0  1  1 0
. x3x . |   6 |   0   3   3   0 |  *  *  * 40  *  * |  1  0  0 1
. x . x |   4 |   0   2   0   2 |  *  *  *  * 60  * |  0  1  0 1
. . x5x |  10 |   0   0   5   5 |  *  *  *  *  * 24 |  0  0  1 1
--------+-----+-----------------+-------------------+-----------
x x3x .   12 |   6   6   6   0 |  3  3  0  2  0  0 | 20  *  * *
x x . x    8 |   4   4   0   4 |  2  0  2  0  2  0 |  * 30  * *
x . x5x   20 |  10   0  10  10 |  0  5  5  0  0  2 |  *  * 12 *
. x3x5x  120 |   0  60  60  60 |  0  0  0 20 30 12 |  *  *  * 2

snubbed forms: x s3s5s, s2s3s5s

xx3xx5xx&#x   → height = 1
(grid || grid)


o.3o.5o.    | 120   * |  1  1  1   1  0  0  0 |  1  1  1  1  1  1  0  0  0 | 1  1  1  1 0
.o3.o5.o    |   * 120 |  0  0  0   1  1  1  1 |  0  0  0  1  1  1  1  1  1 | 0  1  1  1 1
------------+---------+-----------------------+----------------------------+-------------
x. .. ..    |   2   0 | 60  *  *   *  *  *  * |  1  1  0  1  0  0  0  0  0 | 1  1  1  0 0
.. x. ..    |   2   0 |  * 60  *   *  *  *  * |  1  0  1  0  1  0  0  0  0 | 1  1  0  1 0
.. .. x.    |   2   0 |  *  * 60   *  *  *  * |  0  1  1  0  0  1  0  0  0 | 1  0  1  1 0
oo3oo5oo&#x |   1   1 |  *  *  * 120  *  *  * |  0  0  0  1  1  1  0  0  0 | 0  1  1  1 0
.x .. ..    |   0   2 |  *  *  *   * 60  *  * |  0  0  0  1  0  0  1  1  0 | 0  1  1  0 1
.. .x ..    |   0   2 |  *  *  *   *  * 60  * |  0  0  0  0  1  0  1  0  1 | 0  1  0  1 1
.. .. .x    |   0   2 |  *  *  *   *  *  * 60 |  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 | 20  *  *  *  *  *  *  *  * | 1  1  0  0 0
x. .. x.    |   4   0 |  2  0  2   0  0  0  0 |  * 30  *  *  *  *  *  *  * | 1  0  1  0 0
.. x.5x.    |  10   0 |  0  5  5   0  0  0  0 |  *  * 12  *  *  *  *  *  * | 1  0  0  1 0
xx .. ..&#x |   2   2 |  1  0  0   2  1  0  0 |  *  *  * 60  *  *  *  *  * | 0  1  1  0 0
.. xx ..&#x |   2   2 |  0  1  0   2  0  1  0 |  *  *  *  * 60  *  *  *  * | 0  1  0  1 0
.. .. xx&#x |   2   2 |  0  0  1   2  0  0  1 |  *  *  *  *  * 60  *  *  * | 0  0  1  1 0
.x3.x ..    |   0   6 |  0  0  0   0  3  3  0 |  *  *  *  *  *  * 20  *  * | 0  1  0  0 1
.x .. .x    |   0   4 |  0  0  0   0  2  0  2 |  *  *  *  *  *  *  * 30  * | 0  0  1  0 1
.. .x5.x    |   0  10 |  0  0  0   0  0  5  5 |  *  *  *  *  *  *  *  * 12 | 0  0  0  1 1
------------+---------+-----------------------+----------------------------+-------------
x.3x.5x.     120   0 | 60 60 60   0  0  0  0 | 20 30 12  0  0  0  0  0  0 | 1  *  *  * *
xx3xx ..&#x    6   6 |  3  3  0   6  3  3  0 |  1  0  0  3  3  0  1  0  0 | * 20  *  * *
xx .. xx&#x    4   4 |  2  0  2   4  2  0  2 |  0  1  0  2  0  2  0  1  0 | *  * 30  * *
.. xx5xx&#x   10  10 |  0  5  5  10  0  5  5 |  0  0  1  0  5  5  0  0  1 | *  *  * 12 *
.x3.x5.x       0 120 |  0  0  0   0 60 60 60 |  0  0  0  0  0  0 20 30 12 | *  *  *  * 1

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