Acronym	dittady
Name	ditrigonary dishecatonicosachoron
Cross sections	©
Circumradius	1
Coordinates	(1, 0, 0, 0)                                         & all permutations, all changes of sign (vertex inscribed q-hex) (1/2, 1/2, 1/2, 1/2)                             & all permutations, all changes of sign (vertex inscribed tes) ((1+sqrt(5))/4, (sqrt(5)-1)/4, 1/4, 0)   & all even permutations, all changes of sign (vertex inscribed v-sadi)
General of army	ex
Colonel of regiment	sishi
Face vector	120, 1200, 2400, 240
Confer	Grünbaumian relatives: dittady+dox   general polytopal classes: Wythoffian polychora
External links

As abstract polytope dittady is automorph, thereby interchanging ike and gike. As such it could be seen to be a non-regular realization of the regular abstract polychoron {3,5,6}.

Incidence matrix according to Dynkin symbol

     x     
   3 |     
     o     
  5 / \ 5/3
   o---o   
     3     

x3o5o3o5/3*b

x . . .      | 120 ♦   20 |   60 |  12  12
-------------+-----+------+------+--------
x . . .      |   2 | 1200 |    6 |   3   3
-------------+-----+------+------+--------
x3o . .      |   3 |    3 | 2400 |   1   1
-------------+-----+------+------+--------
x3o5o .      ♦  12 |   30 |   20 | 120   *
x3o . o5/3*b ♦  12 |   30 |   20 |   * 120

     x     
   3 |     
     o     
  5 / \ 5/2
   o---o   
    3/2    

x3o5o3/2o5/2*b

x . .   .      | 120 ♦   20 |   60 |  12  12
---------------+-----+------+------+--------
x . .   .      |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x3o .   .      |   3 |    3 | 2400 |   1   1
---------------+-----+------+------+--------
x3o5o   .      ♦  12 |   30 |   20 | 120   *
x3o .   o5/2*b ♦  12 |   30 |   20 |   * 120

     x     
   3 |     
     o     
5/4 / \ 5/2
   o---o   
     3     

x3o5/4o3o5/2*b

x .   . .      | 120 ♦   20 |   60 |  12  12
---------------+-----+------+------+--------
x .   . .      |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x3o   . .      |   3 |    3 | 2400 |   1   1
---------------+-----+------+------+--------
x3o5/4o .      ♦  12 |   30 |   20 | 120   *
x3o   . o5/2*b ♦  12 |   30 |   20 |   * 120

     x     
   3 |     
     o     
5/4 / \ 5/3
   o---o   
    3/2    

x3o5/4o3/2o5/3*b

x .   .   .      | 120 ♦   20 |   60 |  12  12
-----------------+-----+------+------+--------
x .   .   .      |   2 | 1200 |    6 |   3   3
-----------------+-----+------+------+--------
x3o   .   .      |   3 |    3 | 2400 |   1   1
-----------------+-----+------+------+--------
x3o5/4o   .      ♦  12 |   30 |   20 | 120   *
x3o   .   o5/3*b ♦  12 |   30 |   20 |   * 120

     x     
 3/2 |     
     o     
  5 / \ 5/3
   o---o   
     3     

x3/2o5o3o5/3*b

x   . . .      | 120 ♦   20 |   60 |  12  12
---------------+-----+------+------+--------
x   . . .      |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x3/2o . .      |   3 |    3 | 2400 |   1   1
---------------+-----+------+------+--------
x3/2o5o .      ♦  12 |   30 |   20 | 120   *
x3/2o . o5/3*b ♦  12 |   30 |   20 |   * 120

     x     
 3/2 |     
     o     
  5 / \ 5/2
   o---o   
    3/2    

x3/2o5o3/2o5/2*b

x   . .   .      | 120 ♦   20 |   60 |  12  12
-----------------+-----+------+------+--------
x   . .   .      |   2 | 1200 |    6 |   3   3
-----------------+-----+------+------+--------
x3/2o .   .      |   3 |    3 | 2400 |   1   1
-----------------+-----+------+------+--------
x3/2o5o   .      ♦  12 |   30 |   20 | 120   *
x3/2o .   o5/2*b ♦  12 |   30 |   20 |   * 120

     x     
 3/2 |     
     o     
5/4 / \ 5/2
   o---o   
     3     

x3/2o5/4o3o5/2*b

x   .   . .      | 120 ♦   20 |   60 |  12  12
-----------------+-----+------+------+--------
x   .   . .      |   2 | 1200 |    6 |   3   3
-----------------+-----+------+------+--------
x3/2o   . .      |   3 |    3 | 2400 |   1   1
-----------------+-----+------+------+--------
x3/2o5/4o .      ♦  12 |   30 |   20 | 120   *
x3/2o   . o5/2*b ♦  12 |   30 |   20 |   * 120

     x     
 3/2 |     
     o     
5/4 / \ 5/3
   o---o   
    3/2    

x3/2o5/4o3/2o5/3*b

x   .   .   .      | 120 ♦   20 |   60 |  12  12
-------------------+-----+------+------+--------
x   .   .   .      |   2 | 1200 |    6 |   3   3
-------------------+-----+------+------+--------
x3/2o   .   .      |   3 |    3 | 2400 |   1   1
-------------------+-----+------+------+--------
x3/2o5/4o   .      ♦  12 |   30 |   20 | 120   *
x3/2o   .   o5/3*b ♦  12 |   30 |   20 |   * 120