ditusna

Acronym ditusna

Name disicosahedronary tetrasnubbachoron,
compound of 20 ex in rahi army,
compound of 2 kidisna

Coxeter symbol 2{3,3;5}[20{3,3,5}]

Circumradius (1+sqrt(5))/2 = 1.618034

©

General of army

rahi

Embedding

                                o3x   x3f F3o   f3f   o3F f3x   x3o                                
                                                                                                   
                        o3o   o3F       F3f             f3F       F3o   o3o                        
                                                                                                   
                                                                                                   
                 o3x o3F   x3V   F3F B3x   V3F       F3V   x3B F3F   V3x   F3o x3o                 
                                                                                                   
                                                                                                   
              x3f       F3F  fC3Bo      D3o   F3B B3F   o3D      Bo3fC  F3F       f3x              
                                                                                                   
            F3o F3f   B3x       o3D   f3C      Dx3xD      C3f   D3o       x3B   f3F o3F            
                                                                                                   
                                                                                                   
         f3f       V3F   D3o f3C         T3o F3C   C3F o3T         C3f o3D   F3V       f3f         
                                                                                                   
                                                                                                   
      o3F             F3B       T3o             B3B             o3T       B3F             F3o      
                                                                                                   
    f3x f3F   F3V   B3F #     F3C      VT3Cx  D3F F3D  Cx3VT      C3F   #   F3B   V3F   F3f x3f    
                      (Dx3xD)                                         (Dx3xD)                      
                                                                                                   
 x3o       x3B   o3D       C3F   B3B D3F                   F3D B3B   F3C       D3o   B3x       o3x 
                                                                                                   
   F3o   F3F       C3f   o3T       F3D       T3f   f3T       D3F       T3o   f3C       F3F   o3F   
                                                                                                   
                                                                                                   
o3o   V3x   #   D3o            Cx3VT      f3T  Go3oG  T3f      VT3Cx            o3D #     x3V   o3o
          (Bo3fC)                                                                 (fC3Bo)          
                                                                                                   
   F3o   F3F       C3f   o3T       F3D       T3f   f3T       D3F       T3o   f3C       F3F   o3F   
                                                                                                   
 x3o       x3B   o3D       C3F   B3B D3F                   F3D B3B   F3C       D3o   B3x       o3x 
                                                                                                   
                      (Dx3xD)                                         (Dx3xD)                      
    f3x f3F   F3V   B3F #     F3C      VT3Cx  D3F F3D  Cx3VT      C3F   #   F3B   V3F   F3f x3f    
                                                                                                   
      o3F             F3B       T3o             B3B             o3T       B3F             F3o      
                                                                                                   
                                                                                                   
         f3f       V3F   D3o f3C         T3o F3C   C3F o3T         C3f o3D   F3V       f3f         
                                                                                                   
                                                                                                   
            F3o F3f   B3x       o3D   f3C      Dx3xD      C3f   D3o       x3B   f3F o3F            
                                                                                                   
              x3f       F3F  fC3Bo      D3o   F3B B3F   o3D      Bo3fC  F3F       f3x              
                                                                                                   
                                                                                                   
                 o3x o3F   x3V   F3F B3x   V3F       F3V   x3B F3F   V3x   F3o x3o                 
                                                                                                   
                                                                                                   
                        o3o   o3F       F3f             f3F       F3o   o3o                        
                                                                                                   
                                o3x   x3f F3o   f3f   o3F f3x   x3o

hull = rahi
(F=ff=f+x, V=2f, B=fff=F+f=2f+x, C=B+x=2F=2f+2x,
D=3f+x, T=FF=3f+2x, G=3F=3f+3x)

                                                f3f                                                
                                                                                                   
                        o3o                                             o3o                        
                                                                                                   
                                                                                                   
                                 F3F                           F3F                                 
                                                                                                   
                                                                                                   
                        F3F                                             F3F                        
                                                                                                   
                                               Dx3xD                                               
                                                                                                   
                                                                                                   
         f3f                                                                           f3f         
                                                                                                   
                                                                                                   
                                                B3B                                                
                                                                                                   
                       Dx3xD                                           Dx3xD                       
                                                                                                   
                                                                                                   
                                 B3B                           B3B                                 
                                                                                                   
         F3F                                                                           F3F         
                                                                                                   
                                                                                                   
o3o                                            Go3oG                                            o3o
                                                                                                   
                                                                                                   
         F3F                                                                           F3F         
                                                                                                   
                                 B3B                           B3B                                 
                                                                                                   
                                                                                                   
                       Dx3xD                                           Dx3xD                       
                                                                                                   
                                                B3B                                                
                                                                                                   
                                                                                                   
         f3f                                                                           f3f         
                                                                                                   
                                                                                                   
                                               Dx3xD                                               
                                                                                                   
                        F3F                                             F3F                        
                                                                                                   
                                                                                                   
                                 F3F                           F3F                                 
                                                                                                   
                                                                                                   
                        o3o                                             o3o                        
                                                                                                   
                                                f3f

vertex-inscribed non-uniform 2 ex compound, infact
10 such components then build this uniform compound.
scaling factor = hf = sqrt[(9+3 sqrt(5))/2] = 2.802517
(vertex figure highlighted)

                o3o                
                                   
        x3o   o3f f3o   o3x        
                                   
                                   
 o3o o3f   f3x       x3f   f3o o3o 
                                   
   f3o       o3F   F3o       o3f   
                                   
                                   
o3x   x3f F3o   f3f   o3F f3x   x3o
                                   
                                   
   f3o       o3F   F3o       o3f   
                                   
 o3o o3f   f3x       x3f   f3o o3o 
                                   
                                   
        x3o   o3f f3o   o3x        
                                   
                o3o

single ex component
(display just slanted by 360°/12=20°)

Confer

blend-component:: ex
compounds:: kidisna

This compound occurs in different forms depending on whether the vertices (coincident by 2) will be counted separately (type A), or will be identified (type C), or whether incident vertices, coplanar triangles, and corealmic tets will be united each (type E). All these would use 20 hexacosachora for compound components. – Two of those cases could be considered on base of the 10 hexacosachora compound (kidisna) instead, i.e. using just 2 such components. That then gives rise to (type B) with no identifications, (type D) with identification of vertices only. – As (type E) already cross-connects the tets of either kidisna, therefore there will be no according type using those for bases here.

The 2-{3} compounds here are inscribed at the equatorial planes of {3}-first oriented ids of the rahi hull. the thereupon built 2-{3}-pyr. compounds (of 2 corealmic tets, red and yellow) then have their tips at the tip of the id adjoint tet of the rahi hull. The remaining tets (of the total compound) are being used in chiral disphenoid symmetry (green and blue), 2 faces of which connect to further such tets (of the same color), the other 2 connect to those 2-{3}-pyr. compounds.

Incidence matrix

(Type A) - no identifications

2400 ♦    12 |    30 |    20 ||  1  verf: ike
-----+-------+-------+-------++---
   2 | 14400 |     5 |     5 ||  1
-----+-------+-------+-------++---
   3 |     3 | 24000 |     2 ||  1
-----+-------+-------+-------++---
   4 |     6 |     4 | 12000 ||  1  tet
-----+-------+-------+-------++---
 120 |   720 |  1200 |   600 || 20  ex

(Type B) - no identifications, but as 2 kidisna comp.

2400 ♦    12 |    30 |    20 || 1  verf: ike
-----+-------+-------+-------++--
   2 | 14400 |     5 |     5 || 1
-----+-------+-------+-------++--
   3 |     3 | 24000 |     2 || 1
-----+-------+-------+-------++--
   4 |     6 |     4 | 12000 || 1  tet
-----+-------+-------+-------++--
1200 |  7200 | 12000 |  6000 || 2  kidisna

(Type C) - identifying incident vertices only

1200 |    24 |    60 |    40 ||  2  verf: face-first 2-ike comp.
-----+-------+-------+-------++---
   2 | 14400 |     5 |     5 ||  1
-----+-------+-------+-------++---
   3 |     3 | 24000 |     2 ||  1
-----+-------+-------+-------++---
   4 |     6 |     4 | 12000 ||  1  tet
-----+-------+-------+-------++---
 120 |   720 |  1200 |   600 || 20  ex

(Type D) - identifying incident vertices only, but as 2 kidisna comp.

1200 |    24 |    60 |    40 || 2  verf: face-first 2-ike comp.
-----+-------+-------+-------++--
   2 | 14400 |     5 |     5 || 1
-----+-------+-------+-------++--
   3 |     3 | 24000 |     2 || 1
-----+-------+-------+-------++--
   4 |     6 |     4 | 12000 || 1  tet
-----+-------+-------+-------++--
1200 |  7200 | 12000 |  6000 || 2  kidisna

(Type E) - identifying vertices, coplanar triangles, and corealmic tets

1200 |   12   12 |    6    36   18 |   14   24 ||  2  verf: face-first 2-ike comp.
-----+-----------+-----------------+-----------++---
   2 | 7200    * |    1     4    0 |    2    3 ||  1  2-{3}-edges
   2 |    * 7200 |    0     2    3 |    2    3 ||  1  2-{3}-pyr. lacings
-----+-----------+-----------------+-----------++---
   6 |    6    0 | 1200     *    * |    2    0 ||  2  2-{3} : orange+magenta edges of verf
   3 |    2    1 |    * 14400    * |    1    1 ||  1  2-{3}-pyr. lateral faces : red+yellow edges of verf
   3 |    0    3 |    *     * 7200 |    0    2 ||  1  mere tet-tet connections : lilaic+lime edges of verf
-----+-----------+-----------------+-----------++---
   7 |    6    6 |    1     6    0 | 2400    * ||  2  2-tet comp. in full axial {6}-pyr. sym.
   4 |    3    3 |    0     2    2 |    * 7200 ||  1  tet
-----+-----------+-----------------+-----------++---
 120 |  360  360 |  120   720  360 |  240  360 || 20  ex

top of page