Acronym madek
Name pentacontatetradisheptacontadipeton,
compound of 2 jak
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art 
     p         p     
                     
        E   O        
                     
p    N         N    p
                     
        O   E        
                     
     p         p     

where:
p = o3o3o *b3o (point)
N = x3o3o *b3o ("normal" hex)
E = o3o3x *b3o ("even" hex)
O = o3o3o *b3x ("odd" hex)
Coordinates
  • (0, 0, 0, 0, 0; sqrt(2/3))                                                                               & all changes of sign
    outermost left and right tips in the lace city
  • (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8); 1/sqrt(24))                    & all even changes of sign in all but the last coord
    innermost right tropical section in the lace city
  • (-1/sqrt(8), -1/sqrt(8), -1/sqrt(8), -1/sqrt(8), -1/sqrt(8); -1/sqrt(24))             & all even changes of sign in all but the last coord
    innermost left tropical section in the lace city
  • (1/sqrt(2), 0, 0, 0, 0; 1/sqrt(6))                                                                    & all permutations in all but the last coord & all changes of sign
    left and right sections underneath the poles in the lace city

Comes in 2 types, depending on the pairs of co-hyperrealmic hix (in dual positioning): being counted separately (type A) or being combined to compounds (stade) as well (type B).


Incidence matrix according to Dynkin symbol

xo3oo3oo3oo3ox *c3oo   (Type A)

o.3o.3o.3o.3o. *c3o.  & | 54 ♦  16 |   80 |  160 |  80  40 |  16 10 || 1
------------------------+----+-----+------+------+---------+--------++--
x. .. .. .. ..    ..  & |  2 | 432 ♦   10 |   30 |  20  10 |   5  5 || 1
------------------------+----+-----+------+------+---------+--------++--
x.3o. .. .. ..    ..  & |  3 |   3 | 1440 ♦    6 |   6   3 |   2  3 || 1
------------------------+----+-----+------+------+---------+--------++--
x.3o.3o. .. ..    ..  & ♦  4 |   6 |    4 | 2160 |   2   1 |   1  2 || 1
------------------------+----+-----+------+------+---------+--------++--
x.3o.3o.3o. ..    ..  & ♦  5 |  10 |   10 |    5 | 864   * |   1  1 || 1
x.3o.3o. .. .. *c3o.  & ♦  5 |  10 |   10 |    5 |   * 432 |   0  2 || 1
------------------------+----+-----+------+------+---------+--------++--
x.3o.3o.3o.3o.    ..  & ♦  6 |  15 |   20 |   15 |   6   0 | 144  * || 1
x.3o.3o.3o. .. *c3o.  & ♦ 10 |  40 |   80 |   80 |  16  16 |   * 54 || 1
------------------------+----+-----+------+------+---------+--------++--
x.3o.3o.3o.3o. *c3o.  & ♦ 27 | 216 |  720 | 1080 | 432 216 |  72 27 || 2


xo3oo3oo3oo3ox *c3oo   (Type B)

o.3o.3o.3o.3o. *c3o.  & | 54 ♦  16 |   80 |  160 |  80  40 | 16 10 || 1
------------------------+----+-----+------+------+---------+-------++--
x. .. .. .. ..    ..  & |  2 | 432 ♦   10 |   30 |  20  10 |  5  5 || 1
------------------------+----+-----+------+------+---------+-------++--
x.3o. .. .. ..    ..  & |  3 |   3 | 1440 ♦    6 |   6   3 |  2  3 || 1
------------------------+----+-----+------+------+---------+-------++--
x.3o.3o. .. ..    ..  & ♦  4 |   6 |    4 | 2160 |   2   1 |  1  2 || 1
------------------------+----+-----+------+------+---------+-------++--
x.3o.3o.3o. ..    ..  & ♦  5 |  10 |   10 |    5 | 864   * |  1  1 || 1
x.3o.3o. .. .. *c3o.  & ♦  5 |  10 |   10 |    5 |   * 432 |  0  2 || 1
------------------------+----+-----+------+------+---------+-------++--
xo3oo3oo3oo3ox    ..    ♦ 12 |  30 |   40 |   30 |  12   0 | 72  * || 2
x.3o.3o.3o. .. *c3o.  & ♦ 10 |  40 |   80 |   80 |  16  16 |  * 54 || 1
------------------------+----+-----+------+------+---------+-------++--
x.3o.3o.3o.3o. *c3o.  & ♦ 27 | 216 |  720 | 1080 | 432 216 | 72 27 || 2

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