Acronym geepy
Name hexacontitetrapeton pyramid,
vertex-first rotunda of gee
Circumradius 1/sqrt(2) = 0.707107
Lace city
in approx. ASCII-art 
    o    		where:
         		o = o3o3o3o4o (point)
o   t   o		t = x3o3o3o4o (tac)

  o  		o = o3o3o3o3o (point)
     		h = x3o3o3o3o (hix)
h   H		H = o3o3o3o3x (dual hix)
Coordinates
  1. (0, 0, 0, 0, 0, 0, 1/sqrt(2))
    tip
  2. (1/sqrt(2), 0, 0, 0, 0, 0, 0)   & permutations and changes of sign in all but last coordinate
    triacontaditeron base
Dihedral angles
  • at hix between hop and hop:   arccos(-5/7) = 135.584691°
  • at hix between hop and gee:   arccos[1/sqrt(7)] = 67.792346°
Face vector 13, 72, 220, 400, 432, 256, 64
Confer
uniform relative:
zee  
general polytopal classes:
segmentoexa   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

ox3oo3oo3oo3oo4oo&#x   → height = 1/sqrt(2) = 0.707107
(pt || gee)

o.3o.3o.3o.3o.4o.    | 1  * ♦ 12  0 | 60   0 | 160   0 | 240   0 | 192  0 | 64 0
.o3.o3.o3.o3.o4.o    | * 12 ♦  1 10 | 10  40 |  40  80 |  80  80 |  80 32 | 32 1
---------------------+------+-------+--------+---------+---------+--------+-----
oo3oo3oo3oo3oo4oo&#x | 1  1 | 12  * ♦ 10   0 |  40   0 |  80   0 |  80  0 | 32 0
.x .. .. .. .. ..    | 0  2 |  * 60 ♦  1   8 |   8  24 |  24  32 |  32 16 | 16 1
---------------------+------+-------+--------+---------+---------+--------+-----
ox .. .. .. .. ..&#x | 1  2 |  2  1 | 60   * ♦   8   0 |  24   0 |  32  0 | 16 0
.x3.o .. .. .. ..    | 0  3 |  0  3 |  * 160 ♦   1   6 |   6  12 |  12  8 |  8 1
---------------------+------+-------+--------+---------+---------+--------+-----
ox3oo .. .. .. ..&#x ♦ 1  3 |  3  3 |  3   1 | 160   * ♦   6   0 |  12  0 |  8 0
.x3.o3.o .. .. ..    ♦ 0  4 |  0  6 |  0   4 |   * 240 ♦   1   4 |   4  4 |  4 1
---------------------+------+-------+--------+---------+---------+--------+-----
ox3oo3oo .. .. ..&#x ♦ 1  4 |  4  6 |  6   4 |   4   1 | 240   * |   4  0 |  4 0
.x3.o3.o3.o .. ..    ♦ 0  5 |  0 10 |  0  10 |   0   5 |   * 192 |   1  2 |  2 1
---------------------+------+-------+--------+---------+---------+--------+-----
ox3oo3oo3oo .. ..&#x ♦ 1  5 |  5 10 | 10  10 |  10   5 |   5   1 | 192  * |  2 0
.x3.o3.o3.o3.o ..    ♦ 0  6 |  0 15 |  0  20 |   0  15 |   0   6 |   * 64 |  1 1
---------------------+------+-------+--------+---------+---------+--------+-----
ox3oo3oo3oo3oo ..&#x ♦ 1  6 |  6 15 | 15  20 |  20  15 |  15   6 |   6  1 | 64 *
.x3.o3.o3.o3.o4.o    ♦ 0 12 |  0 60 |  0 160 |   0 240 |   0 192 |   0 64 |  * 1


oo3oo3oo *b3oo3oo3ox&#x   → height = 1/sqrt(2) = 0.707107
(pt || gee)

o.3o.3o. *b3o.3o.3o.    | 1  * ♦ 12  0 | 60   0 | 160   0 | 240   0 | 192  0  0 | 32 32 0
.o3.o3.o *b3.o3.o3.o    | * 12 ♦  1 10 | 10  40 |  40  80 |  80  80 |  80 16 16 | 16 16 1
------------------------+------+-------+--------+---------+---------+-----------+--------
oo3oo3oo *b3oo3oo3oo&#x | 1  1 | 12  * ♦ 10   0 |  40   0 |  80   0 |  80  0  0 | 16 16 0
.. .. ..    .. .. .x    | 0  2 |  * 60 ♦  1   8 |   8  24 |  24  32 |  32  8  8 |  8  8 1
------------------------+------+-------+--------+---------+---------+-----------+--------
.. .. ..    .. .. ox&#x | 1  2 |  2  1 | 60   * ♦   8   0 |  24   0 |  32  0  0 |  8  8 0
.. .. ..    .. .o3.x    | 0  3 |  0  3 |  * 160 ♦   1   6 |   6  12 |  12  4  4 |  4  4 1
------------------------+------+-------+--------+---------+---------+-----------+--------
.. .. ..    .. oo3ox&#x ♦ 1  3 |  3  3 |  3   1 | 160   * ♦   6   0 |  12  0  0 |  4  4 0
.. .. ..    .o3.o3.x    ♦ 0  4 |  0  6 |  0   4 |   * 240 ♦   1   4 |   4  2  2 |  2  2 1
------------------------+------+-------+--------+---------+---------+-----------+--------
.. .. ..    oo3oo3ox&#x ♦ 1  4 |  4  6 |  6   4 |   4   1 | 240   * |   4  0  0 |  2  2 0
.. .o .. *b3.o3.o3.x    ♦ 0  5 |  0 10 |  0  10 |   0   5 |   * 192 |   1  1  1 |  1  1 1
------------------------+------+-------+--------+---------+---------+-----------+--------
.. oo .. *b3oo3oo3ox&#x ♦ 1  5 |  5 10 | 10  10 |  10   5 |   5   1 | 192  *  * |  1  1 0
.o3.o .. *b3.o3.o3.x    ♦ 0  6 |  0 15 |  0  20 |   0  15 |   0   6 |   * 32  * |  1  0 1
.. .o3.o *b3.o3.o3.x    ♦ 0  6 |  0 15 |  0  20 |   0  15 |   0   6 |   *  * 32 |  0  1 1
------------------------+------+-------+--------+---------+---------+-----------+--------
oo3oo .. *b3oo3oo3ox&#x ♦ 1  6 |  6 15 | 15  20 |  20  15 |  15   6 |   6  1  0 | 32  * *
.. oo3oo *b3oo3oo3ox&#x ♦ 1  6 |  6 15 | 15  20 |  20  15 |  15   6 |   6  0  1 |  * 32 *
.o3.o3.o *b3.o3.o3.x    ♦ 0 12 |  0 60 |  0 160 |   0 240 |   0 192 |   0 32 32 |  *  * 1

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