pedisna

Acronym pedisna

Name pental disnubbachoron,
compound of 12 ex in rox army,
compound of 2 kepisna

Coxeter symbol 2{3;3,5}[12{3,3,5}]

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

©

General of army

rox

Embedding

                                            o5o                                            
                                    x5o             x5o                                    
                                            o5f                                            
                        o5x                                     o5x                        
                o5o             x5x                     x5x             o5o                
                                                                                           
                    f5o                     x5f                     f5o                    
            o5x                     F5o             F5o                     o5x            
                                o5F                     o5F                                
                        f5x                                     f5x                        
                                                                                           
            x5x                     f5f             f5f                     x5x            
    x5o             o5F                     V5o                     o5F             x5o    
                                                                                           
                F5o             o5V                     o5V             F5o                
o5o                     f5f                                     f5f                     o5o
    o5f                                     x5F                                     o5f    
            x5f                     F5x             F5x                     x5f            
                                                                                           
x5o                     V5o                                     V5o                     x5o
                                x5F                     x5F                                
            F5o                                                             F5o            
    x5x             f5f                    oA5Ao                    f5f             x5x    
            o5F                                                             o5F            
                                F5x                     F5x                                
o5x                     o5V                                     o5V                     o5x
                                                                                           
            f5x                     x5F             x5F                     f5x            
    f5o                                     F5x                                     f5o    
o5o                     f5f                                     f5f                     o5o
                o5F             V5o                     V5o             o5F                
                                                                                           
    o5x             F5o                     o5V                     F5o             o5x    
            x5x                     f5f             f5f                     x5x            
                                                                                           
                        x5f                                     x5f                        
                                F5o                     F5o                                
            x5o                     o5F             o5F                     x5o            
                    o5f                     f5x                     o5f                    
                                                                                           
                o5o             x5x                     x5x             o5o                
                        x5o                                     x5o                        
                                            f5o                                            
                                    o5x             o5x                                    
                                            o5o

hull = rox
(F=ff=f+x, V=2f, A=F+x)

                                            o5o                                            
                                                                                           
                                                                                           
                                                                                           
                o5o             x5x                     x5x             o5o                
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
            x5x                     f5f             f5f                     x5x            
                                                                                           
                                                                                           
                                                                                           
o5o                     f5f                                     f5f                     o5o
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
    x5x             f5f                    oA5Ao                    f5f             x5x    
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
o5o                     f5f                                     f5f                     o5o
                                                                                           
                                                                                           
                                                                                           
            x5x                     f5f             f5f                     x5x            
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                                                                                           
                o5o             x5x                     x5x             o5o                
                                                                                           
                                                                                           
                                                                                           
                                            o5o

vertex-inscribed non-uniform 2 ex compound, infact
6 such components then build this uniform compound.
scaling factor = x(10,2) = sqrt[(5+sqrt(5))/2] = 1.902113
(vertex figure highlighted)

                 o5o           o5o                 
                        o5x                        
                                                   
            x5o                     x5o            
     o5o                                   o5o     
                        f5o                        
                 o5f           o5f                 
                                                   
     o5x                                   o5x     
            f5o                     f5o            
                                                   
o5o                     x5x                     o5o
                                                   
            o5f                     o5f            
     x5o                                   x5o     
                                                   
                 f5o           f5o                 
                        o5f                        
     o5o                                   o5o     
            o5x                     o5x            
                                                   
                        x5o                        
                 o5o           o5o

single ex component
(display just slanted by 360°/20=18°)

Confer

blend-component:: ex
compounds:: kepisna

External
links

This compound occurs in 6 different forms depending on whether the vertices (coincident by 2) will be counted separately (type A), or will be identified while the incident edges will still be counted separately (type C), or whether both would be identified (type E). All these would use 12 hexacosachora for compound components. – Each of those cases could be considered on base of the 6 hexacosachora compound (kepisna) 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, and (type F) with identifications of coincident vertices and concident edges.

From the 3rd and 4th line of the matrices (type E) or (type F) one moreover reads off that each rosette of 5 tets around those normal edges uses orange-green-orange-green-orange in cyclical order as incident faces. One double edge then would emanate from the top vertex of the axial edge along the green incident face, while the other double edge would emanate from the bottom vertex along the other green incident face. A third double edge then would be located at the outer rim of that rosette between the tips of the 2 neighboring incident orange faces. – This then tells furthermore that on either side of the top double edge a green face each is on the upper side of the rosette, that on either side of the bottom double edge there is a green face each on the lower side of the rosette, and that on either side of the double edge at the rim also will be a green face each, one on the upper, one on the lower side of that rosette. All remaining upper and lower faces of that rosette then will be orange (2 each). – The same holds for the cyan and magenta faces, building similar rosettes around each normal edge, but showing up the opposite handedness instead.

Incidence matrix

(Type A) - no identifications

1440 ♦   12 |    30 |   20 ||  1  verf: ike
-----+------+-------+------++---
   2 | 8640 |     5 |    5 ||  1
-----+------+-------+------++---
   3 |    3 | 14400 |    2 ||  1
-----+------+-------+------++---
   4 |    6 |     4 | 7200 ||  1  tet
-----+------+-------+------++---
 120 |  720 |  1200 |  600 || 12  ex

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

1440 ♦   12 |    30 |   20 || 1  verf: ike
-----+------+-------+------++--
   2 | 8640 |     5 |    5 || 1
-----+------+-------+------++--
   3 |    3 | 14400 |    2 || 1
-----+------+-------+------++--
   4 |    6 |     4 | 7200 || 1  tet
-----+------+-------+------++--
 720 | 4320 |  7200 | 3600 || 2  kepisna

(Type C) - identifying incident vertices only 

720 ♦   24 |    60 |   40 ||  2  verf: twirled vertex-first 2-ike comp., with no identifications
----+------+-------+------++---
  2 | 8640 |     5 |    5 ||  1
----+------+-------+------++---
  3 |    3 | 14400 |    2 ||  1
----+------+-------+------++---
  4 |    6 |     4 | 7200 ||  1  tet
----+------+-------+------++---
120 |  720 |  1200 |  600 || 12  ex

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

720 ♦   24 |    60 |   40 || 2  verf: twirled vertex-first 2-ike comp., with no identifications
----+------+-------+------++--
  2 | 8640 |     5 |    5 || 1
----+------+-------+------++--
  3 |    3 | 14400 |    2 || 1
----+------+-------+------++--
  4 |    6 |     4 | 7200 || 1  tet
----+------+-------+------++--
720 | 4320 |  7200 | 3600 || 2  kepisna

(Type E) - identifying vertices and coincident edges

720 ♦   2   10   10 |   15   15   15   15 |   20   20 || 1 1  verf: twirled vertex-first 2-ike comp., with identifications
----+---------------+---------------------+-----------++----
  2 | 720    *    * |    5    5    0    0 |    5    5 || 1 1  edge-fig: decagonal 2-{5} comp., acc. to coinc. vert. of verf
  2 |   * 3600    * |    2    0    3    0 |    5    0 || 1 0  acc. to unique vertices of red ike of verf
  2 |   *    * 3600 |    0    2    0    3 |    0    5 || 0 1  acc. to unique vertices of yellow ike of verf
----+---------------+---------------------+-----------++----
  3 |   1    2    0 | 3600    *    *    * |    2    0 || 1 0  green, acc. to green edges of verf
  3 |   1    0    2 |    * 3600    *    * |    0    2 || 0 1  cyan, acc. to cyan edges of verf
  3 |   0    3    0 |    *    * 3600    * |    2    0 || 1 0  orange, acc. to orange edges of verf
  3 |   0    0    3 |    *    *    * 3600 |    0    2 || 0 1  magenta, acc. to magenta edges of verf
----+---------------+---------------------+-----------++----
  4 |   1    5    0 |    2    0    2    0 | 3600    * || 1 0  green-green-orange-orange, tet (as 2-ap), of red ex
  4 |   1    0    5 |    0    2    0    2 |    * 3600 || 0 1  cyan-cyan-magenta-magenta, tet (as 2-ap), of yellow ex
----+---------------+---------------------+-----------++----
120 | 120  600    0 |  600    0  600    0 |  600    0 || 6 *  red ex
120 | 120    0  600 |    0  600    0  600 |    0  600 || * 6  yellow ex

(Type F) - identifying vertices and coincident edges, but as 2 kepisna comp.

720 ♦   2   10   10 |   15   15   15   15 |   20   20 || 1 1  verf: twirled vertex-first 2-ike comp., with identifications
----+---------------+---------------------+-----------++----
  2 | 720    *    * |    5    5    0    0 |    5    5 || 1 1  edge-fig: decagonal 2-{5} comp., acc. to coinc. vert. of verf
  2 |   * 3600    * |    2    0    3    0 |    5    0 || 1 0  acc. to unique vertices of red ike of verf
  2 |   *    * 3600 |    0    2    0    3 |    0    5 || 0 1  acc. to unique vertices of yellow ike of verf
----+---------------+---------------------+-----------++----
  3 |   1    2    0 | 3600    *    *    * |    2    0 || 1 0  green, acc. to green edges of verf
  3 |   1    0    2 |    * 3600    *    * |    0    2 || 0 1  cyan, acc. to cyan edges of verf
  3 |   0    3    0 |    *    * 3600    * |    2    0 || 1 0  orange, acc. to orange edges of verf
  3 |   0    0    3 |    *    *    * 3600 |    0    2 || 0 1  magenta, acc. to magenta edges of verf
----+---------------+---------------------+-----------++----
  4 |   1    5    0 |    2    0    2    0 | 3600    * || 1 0  green-green-orange-orange, tet (as 2-ap), of red kepisna
  4 |   1    0    5 |    0    2    0    2 |    * 3600 || 0 1  cyan-cyan-magenta-magenta, tet (as 2-ap), of yellow kepisna
----+---------------+---------------------+-----------++----
720 | 720 3600    0 | 3600    0 3600    0 | 3600    0 || 1 *  red kepisna
720 | 720    0 3600 |    0 3600    0 3600 |    0 3600 || * 1  yellow kepisna

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