Acronym phexid
Name partially hexa-expanded icosidodecahedron
  
 ©
Vertex figure [(3,5)2], [3,4,h,5], [4,5,H]
Lace city
in approx. ASCII-art 
                o                
           f         f           
      x                   x      
           A         A           		where:
                                 		C=A+f=2f+q
  x                           x  		B=A+x=f+q+x
     F   B             B   F     		A=f+q
                                 		F=ff=f+x
o               C               o
                                 
     F   B             B   F     
  x                           x  
                                 
           A         A           
      x                   x      
           f         f           
                o
Coordinates
  1. (C, 0, 0)/2           & all permutations, all changes of sign
    ([(3,5)2] type vertices)
  2. (x, f, B)/2            & all cyclic permutations, all changes of sign
    ([3,4,h,5] type vertices)
  3. (x, A, F)/2           & all cyclic permutations, all changes of sign
    ([4,5,H] type vertices)
where C=A+f=2f+q, B=A+x=f+q+x, A=f+q, F=ff=f+x
Face vector 54, 96, 44
Confer
uniform variant:
id
general polytopal classes:
partial Stott expansions  

The semiregular shield hexagon {(h,H)3} has alternating corner angles h = arccos[(3-sqrt(5))/sqrt(32)] = 82.238756° resp. H = arccos[-(3+sqrt(5))/sqrt(32)] = 157.761244°.


Incidence matrix

6  *  * |  4  0  0  0  0 |  2  2  0 0  [(3,5)2]
* 24  * |  1  1  1  1  0 |  1  1  1 1  [3,4,h,5]
*  * 24 |  0  0  1  1  1 |  0  1  1 1  [4,5,H]
--------+----------------+-----------
1  1  0 | 24  *  *  *  * |  1  1  0 0
0  2  0 |  * 12  *  *  * |  1  0  1 0
0  1  1 |  *  * 24  *  * |  0  0  1 1  {4}-{(h,H)3}
0  1  1 |  *  *  * 24  * |  0  1  0 1  {5}-{(h,H)3}
0  0  2 |  *  *  *  * 12 |  0  1  1 0
--------+----------------+-----------
1  2  0 |  2  1  0  0  0 | 12  *  * *
1  2  2 |  2  0  0  2  1 |  * 12  * *
0  2  2 |  0  1  2  0  1 |  *  * 12 *
0  3  3 |  0  0  3  3  0 |  *  *  * 8  {(h,H)3}

© 2004-2024
top of page