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


xoo3ooo3ooo3ooo3oxo&#x   → height(1,2) = 1/sqrt(3) = 0.577350
                           height(1,3) = height(2,3) = sqrt(7/12) = 0.763763

o..3o..3o..3o..3o..    & | 12 * ♦  5  5  1 | 10  30  5  5 | 10  40 30 10  30 |  5 25  50 10  40 30 | 1  6 15 10  5 25  50 | 1 1  6 15 10
..o3..o3..o3..o3..o      |  * 1 ♦  0  0 12 |  0   0 30 30 |  0   0  0 40 120 |  0  0   0 30 120 90 | 0  0  0  0 12 60 120 | 0 2 12 30 20
-------------------------+------+----------+--------------+------------------+---------------------+----------------------+-------------
x.. ... ... ... ...    & |  2 0 | 30  *  * ♦  4   4  1  0 |  6  12  6  4   4 |  4 12  16  6  12  6 | 1  4  7  4  4 12  16 | 1 1  4  7  4
oo.3oo.3oo.3oo.3oo.&#x   |  2 0 |  * 30  * ♦  0   8  0  1 |  0  12 12  0   8 |  0  8  24  0  12 12 | 0  2  8  6  0  8  24 | 1 0  2  8  6
o.o3o.o3o.o3o.o3o.o&#x & |  1 1 |  *  * 12 ♦  0   0  5  5 |  0   0  0 10  30 |  0  0   0 10  40 30 | 0  0  0  0  5 25  50 | 0 1  6 15 10
-------------------------+------+----------+--------------+------------------+---------------------+----------------------+-------------
x..3o.. ... ... ...    & |  3 0 |  3  0  0 | 40   *  *  * ♦  3   3  0  1   0 |  3  6   3  3   3  0 | 1  3  3  1  3  6   3 | 1 1  3  3  1
xo. ... ... ... ...&#x & |  3 0 |  1  2  0 |  * 120  *  * ♦  0   3  3  0   1 |  0  3   9  0   3  3 | 0  1  4  3  0  3   9 | 1 0  1  4  3
x.o ... ... ... ...&#x & |  2 1 |  1  0  2 |  *   * 30  * ♦  0   0  0  4   4 |  0  0   0  6  12  6 | 0  0  0  0  4 12  16 | 0 1  4  7  4
ooo3ooo3ooo3ooo3ooo&#x   |  2 1 |  0  1  2 |  *   *  * 30 ♦  0   0  0  0   8 |  0  0   0  0  12 12 | 0  0  0  0  0  8  24 | 0 0  2  8  6
-------------------------+------+----------+--------------+------------------+---------------------+----------------------+-------------
x..3o..3o.. ... ...    & ♦  4 0 |  6  0  0 |  4   0  0  0 | 30   *  *  *   * ♦  2  2   0  1   0  0 | 1  2  1  0  2  2   0 | 1 1  2  1  0
xo.3oo. ... ... ...&#x & ♦  4 0 |  3  3  0 |  1   3  0  0 |  * 120  *  *   * ♦  0  2   2  0   1  0 | 0  1  2  1  0  2   2 | 1 0  1  2  1
xo. ... ... ... ox.&#x   ♦  4 0 |  2  4  0 |  0   4  0  0 |  *   * 90  *   * ♦  0  0   4  0   0  1 | 0  0  2  2  0  0   4 | 1 0  0  2  2
x.o3o.o ... ... ...&#x & ♦  3 1 |  3  0  3 |  1   0  3  0 |  *   *  * 40   * ♦  0  0   0  3   3  0 | 0  0  0  0  3  6   3 | 0 1  3  3  1
xoo ... ... ... ...&#x & ♦  3 1 |  1  2  3 |  0   1  1  2 |  *   *  *  * 120 ♦  0  0   0  0   3  3 | 0  0  0  0  0  3   9 | 0 0  1  4  3
-------------------------+------+----------+--------------+------------------+---------------------+----------------------+-------------
x..3o..3o..3o.. ...    & ♦  5 0 | 10  0  0 | 10   0  0  0 |  5   0  0  0   0 | 12  *   *  *   *  * | 1  1  0  0  1  0   0 | 1 1  1  0  0
xo.3oo.3oo. ... ...&#x & ♦  5 0 |  6  4  0 |  4   6  0  0 |  1   4  0  0   0 |  * 60   *  *   *  * | 0  1  1  0  0  1   0 | 1 0  1  1  0
xo.3oo. ... ... ox.&#x & ♦  5 0 |  4  6  0 |  1   9  0  0 |  0   2  3  0   0 |  *  * 120  *   *  * | 0  0  1  1  0  0   1 | 1 0  0  1  1
x.o3o.o3o.o ... ...&#x & ♦  4 1 |  6  0  4 |  4   0  6  0 |  1   0  0  4   0 |  *  *   * 30   *  * | 0  0  0  0  2  2   0 | 0 1  2  1  0
xoo3ooo ... ... ...&#x & ♦  4 1 |  3  3  4 |  1   3  3  3 |  0   1  0  1   3 |  *  *   *  * 120  * | 0  0  0  0  0  2   2 | 0 0  1  2  1
xoo ... ... ... oxo&#x   ♦  4 1 |  2  4  4 |  0   4  2  4 |  0   0  1  0   4 |  *  *   *  *   * 90 | 0  0  0  0  0  0   4 | 0 0  0  2  2
-------------------------+------+----------+--------------+------------------+---------------------+----------------------+-------------
x..3o..3o..3o..3o..    & ♦  6 0 | 15  0  0 | 20   0  0  0 | 15   0  0  0   0 |  6  0   0  0   0  0 | 2  *  *  *  *  *   * | 1 1  0  0  0
xo.3oo.3oo.3oo. ...&#x & ♦  6 0 | 10  5  0 | 10  10  0  0 |  5  10  0  0   0 |  1  5   0  0   0  0 | * 12  *  *  *  *   * | 1 0  1  0  0
xo.3oo.3oo. ... ox.&#x & ♦  6 0 |  7  8  0 |  4  16  0  0 |  1   8  6  0   0 |  0  2   4  0   0  0 | *  * 30  *  *  *   * | 1 0  0  1  0
xo.3oo. ... oo.3ox.&#x   ♦  6 0 |  6  9  0 |  2  18  0  0 |  0   6  9  0   0 |  0  0   6  0   0  0 | *  *  * 20  *  *   * | 1 0  0  0  1
x.o3o.o3o.o3o.o ...&#x & ♦  5 1 | 10  0  5 | 10   0 10  0 |  5   0  0 10   0 |  1  0   0  5   0  0 | *  *  *  * 12  *   * | 0 1  1  0  0
xoo3ooo3ooo ... ...&#x & ♦  5 1 |  6  4  5 |  4   6  6  4 |  1   4  0  4   6 |  0  1   0  1   4  0 | *  *  *  *  * 60   * | 0 0  1  1  0
xoo3ooo ... ... oxo&#x & ♦  5 1 |  4  6  5 |  1   9  4  6 |  0   2  3  1   9 |  0  0   1  0   2  3 | *  *  *  *  *  * 120 | 0 0  0  1  1
-------------------------+------+----------+--------------+------------------+---------------------+----------------------+-------------
xo.3oo.3oo.3oo.3ox.&#x   ♦ 12 0 | 30 30  0 | 40 120  0  0 | 30 120 90  0   0 | 12 60 120  0   0  0 | 2 12 30 20  0  0   0 | 1 *  *  *  *
x.o3o.o3o.o3o.o3o.o&#x & ♦  6 1 | 15  0  6 | 20   0 15  0 | 15   0  0 20   0 |  6  0   0 15   0  0 | 1  0  0  0  6  0   0 | * 2  *  *  *
xoo3ooo3ooo3ooo ...&#x & ♦  6 1 | 10  5  6 | 10  10 10  5 |  5  10  0 10  10 |  1  5   0  5  10  0 | 0  1  0  0  1  5   0 | * * 12  *  *
xoo3ooo3ooo ... oxo&#x & ♦  6 1 |  7  8  6 |  4  16  7  8 |  1   8  6  4  16 |  0  2   4  1   8  6 | 0  0  1  0  0  2   4 | * *  * 30  *
xoo3ooo ... ooo3oxo&#x   ♦  6 1 |  6  9  6 |  2  18  6  9 |  0   6  9  2  18 |  0  0   6  0   6  9 | 0  0  0  1  0  0   6 | * *  *  * 20

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