Acronym disti
Name disnub tetrakisicositetrachoron
Circumradius (1+sqrt(5))/2 = 1.618034
Lace city
in approx. ASCII-art 
        ox2xo fo2of   xf2fx   fo2of ox2xo        
                                                 
                                                 
                                                 
xo2ox         oF2Fo   Fx2xF   oF2Fo         xo2ox
                                                 
                                                 
of2fo   Fo2oF         fF2Ff         Fo2oF   of2fo
                                                 
                                                 
                                                 
fx2xf   xF2Fx Ff2fF           Ff2fF xF2Fx   fx2xf
                                                 
                                                 
                                                 
of2fo   Fo2oF         fF2Ff         Fo2oF   of2fo
                                                 
                                                 
xo2ox         oF2Fo   Fx2xF   oF2Fo         xo2ox
                                                 
                                                 
                                                 
        ox2xo fo2of   xf2fx   fo2of ox2xo
Coordinates (τ2/2, τ/2, 1/2, 0)    & all permutations, all changes of sign
where τ = (1+sqrt(5))/2
Vertex figure 
 ©
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: siddo so tet
sadi 2424192
)
Dihedral angles
  • at {3} between so and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between siddo and tet:   arccos[-sqrt(5/8)] = 142.238756°
  • at {3} between siddo and siddo:   120°

Sadi itself was obtained from ex by the diminishing at the facet realms of an ico. This compound is obtained by adding its gyrated mirror image, while leaving those facet realms in place. Thus all ikes will compound in turn into siddoes and furthermore the isolated 24 tets (in the respective dual positions) also compound into soes as well.

However there also is a different compound of 2 sadis, where then the ikes won't compound, rather they will be located in the facet realms of a cont instead.


Incidence matrix according to Dynkin symbol

β3β4o3o

both( . . . . ) | 192 ♦   3   6 |  3   9   3 |  3  1   4
----------------+-----+---------+------------+----------
      . β4o .   |   2 | 288   * |  0   2   2 |  1  1   2
sefa( β3β . . ) |   2 |   * 576 |  1   2   0 |  2  0   1
----------------+-----+---------+------------+----------
      β3β . .   ♦   6 |   0   6 | 96   *   * |  2  0   0  2{3}
sefa( β3β4o . ) |   3 |   1   2 |  * 576   * |  1  0   1
sefa( . β4o3o ) |   3 |   3   0 |  *   * 192 |  0  1   1
----------------+-----+---------+------------+----------
      β3β4o .   ♦  24 |  12  48 |  8  24   0 | 24  *   *
      . β4o3o   ♦   8 |  12   0 |  0   0   8 |  * 24   *
sefa( β3β4o3o ) ♦   4 |   3   3 |  0   3   1 |  *  * 192

starting figure: x3x4o3o

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