Acronym hinpy
Name demipenteractic pyramid,
vertex pyramid of jak
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art
o    	where: o = o3o3o *b3o (point)
    E	       E = o3o3x *b3o (hex)
X    	       X = x3o3o *b3o
Coordinates
  1. (0, 0, 0, 0, 0, sqrt(3/8))
    tip
  2. (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 0)   & even permutations and even changes of sign in one but last coord.
    base
Dihedral angles
(at margins)
  • at hex between hexpy and hin:   60°
  • at pen between hin and hix:   arccos[sqrt(3/8)] = 52.238756°
  • ...
Confer
uniform relative:
jak  
related CRFs:
hint  
general polytopal classes:
segmentopeta   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

oo3oo3oo3ox *c3oo&#x   → height = sqrt(3/8) = 0.612372
(pt || hin)

o.3o.3o.3o. *c3o.    | 1  *  16  0 | 80   0 | 160  0  0 | 80 40  0  0 | 10 16 0
.o3.o3.o3.o *c3.o    | * 16   1 10 | 10  30 |  30 20 10 | 20 10  5  5 |  5  5 1
---------------------+------+-------+--------+-----------+-------------+--------
oo3oo3oo3oo *c3oo&#x | 1  1 | 16  *  10   0 |  30  0  0 | 20 10  0  0 |  5  5 0
.. .. .. .x    ..    | 0  2 |  * 80   1   6 |   6  6  3 |  6  3  2  3 |  4  2 1
---------------------+------+-------+--------+-----------+-------------+--------
.. .. .. ox    ..&#x | 1  2 |  2  1 | 80   *    6  0  0 |  6  3  0  0 |  3  2 0
.. .. .o3.x    ..    | 0  3 |  0  3 |  * 160 |   1  2  1 |  2  1  1  2 |  2  1 1
---------------------+------+-------+--------+-----------+-------------+--------
.. .. oo3ox    ..&#x  1  3 |  3  3 |  3   1 | 160  *  * |  2  1  0  0 |  2  1 0
.. .o3.o3.x    ..     0  4 |  0  6 |  0   4 |   * 80  * |  1  0  1  1 |  1  1 1
.. .. .o3.x *c3.o     0  4 |  0  6 |  0   4 |   *  * 40 |  0  1  0  2 |  2  0 1
---------------------+------+-------+--------+-----------+-------------+--------
.. oo3oo3ox    ..&#x  1  4 |  4  6 |  6   4 |   4  1  0 | 80  *  *  * |  1  1 0
.. .. oo3ox *c3oo&#x  1  4 |  4  6 |  6   4 |   4  0  1 |  * 40  *  * |  2  0 0
.o3.o3.o3.x    ..     0  5 |  0 10 |  0  10 |   0  5  0 |  *  * 16  * |  0  1 1
.. .o3.o3.x *c3.o     0  8 |  0 24 |  0  32 |   0  8  8 |  *  *  * 10 |  1  0 1  
---------------------+------+-------+--------+-----------+-------------+--------
.. oo3oo3ox *c3oo&#x  1  8 |  8 24 | 24  32 |  32  8  8 |  8  8  0  1 | 10  * *
oo3oo3oo3ox    ..&#x  1  5 |  5 10 | 10  10 |  10  5  0 |  5  0  1  0 |  * 16 *
.o3.o3.o3.x *c3.o     0 16 |  0 80 |  0 160 |   0 80 40 |  0  0 16 10 |  *  * 1

oxo3ooo3oox oxo oox&#x   → height(1,2) = height(1,3) = sqrt(3/8) = 0.612372
                           height(2,3) = 0
(pt || tegum sum of 2 mutually inverted, lacings-orthogonal tepes)

o..3o..3o.. o.. o..      | 1  *  16  0 0  0 | 24 8 48  0  0  0 | 16 96 48 0  0  0  0  0 | 4 32 24 48 12 0  0 0 | 4 16 6 0
.o.3.o.3.o. .o. .o.    & | * 16   1  3 1  6 |  3 1  6  3 18  9 |  3 18  9 1  8  6 12  3 | 1  8  6 12  3 2  5 3 | 2  5 3 1
-------------------------+------+------------+------------------+------------------------+----------------------+---------
oo.3oo.3oo. oo. oo.&#x & | 1  1 | 16  * *  *   3 1  6  0  0  0 |  3 18  9 0  0  0  0  0 | 1  8  6 12  3 0  0 0 | 2  5 3 0
.x. ... ... ... ...    & | 0  2 |  * 24 *  *   1 0  0  2  4  0 |  2  4  0 1  4  2  2  0 | 1  4  2  2  0 2  2 1 | 2  2 1 1
... ... ... .x. ...    & | 0  2 |  *  * 8  *   0 1  0  0  0  6 |  0  0  6 0  0  0  6  3 | 0  0  0  6  3 0  2 3 | 0  2 3 1
.oo3.oo3.oo .oo .oo&#x   | 0  2 |  *  * * 48   0 0  1  0  4  2 |  0  4  2 0  2  2  4  1 | 0  2  2  4  1 1  2 2 | 1  2 2 1
-------------------------+------+------------+------------------+------------------------+----------------------+---------
ox. ... ... ... ...&#x & | 1  2 |  2  1 0  0 | 24 *  *  *  *  *   2  4  0 0  0  0  0  0 | 1  4  2  2  0 0  0 0 | 2  2 1 0
... ... ... ox. ...&#x & | 1  2 |  2  0 1  0 |  * 8  *  *  *  *   0  0  6 0  0  0  0  0 | 0  0  0  6  3 0  0 0 | 0  2 3 0
ooo3ooo3ooo ooo ooo&#x   | 1  2 |  2  0 0  1 |  * * 48  *  *  *   0  4  2 0  0  0  0  0 | 0  2  2  4  1 0  0 0 | 1  2 2 0
.x.3.o. ... ... ...    & | 0  3 |  0  3 0  0 |  * *  * 16  *  * |  1  0  0 1  2  0  0  0 | 1  2  0  0  0 2  1 0 | 2  1 0 1
.xo ... ... ... ...&#x & | 0  3 |  0  1 0  2 |  * *  *  * 96  * |  0  1  0 0  1  1  1  0 | 0  1  1  1  0 1  1 1 | 1  1 1 1
... ... ... .xo ...&#x & | 0  3 |  0  0 1  2 |  * *  *  *  * 48 |  0  0  1 0  0  0  2  1 | 0  0  0  2  1 0  1 2 | 0  1 2 1
-------------------------+------+------------+------------------+------------------------+----------------------+---------
ox.3oo. ... ... ...&#x &  1  3 |  3  3 0  0 |  3 0  0  1  0  0 | 16  *  * *  *  *  *  * | 1  2  0  0  0 0  0 0 | 2  1 0 0
oxo ... ... ... ...&#x &  1  3 |  3  1 0  2 |  1 0  2  0  1  0 |  * 96  * *  *  *  *  * | 0  1  1  1  0 0  0 0 | 1  1 1 0
... ... ... oxo ...&#x &  1  3 |  3  0 1  2 |  0 1  2  0  0  1 |  *  * 48 *  *  *  *  * | 0  0  0  2  1 0  0 0 | 0  1 2 0
.x.3.o.3.o. ... ...    &  0  4 |  0  6 0  0 |  0 0  0  4  0  0 |  *  *  * 4  *  *  *  * | 1  0  0  0  0 2  0 0 | 2  0 0 1
.xo3.oo ... ... ...&#x &  0  4 |  0  3 0  3 |  0 0  0  1  3  0 |  *  *  * * 32  *  *  * | 0  1  0  0  0 1  1 0 | 1  1 0 1
.xo ... .ox ... ...&#x    0  4 |  0  2 0  4 |  0 0  0  0  4  0 |  *  *  * *  * 24  *  * | 0  0  1  0  0 1  0 1 | 1  0 1 1
.xo ... ... ... .ox&#x &  0  4 |  0  1 1  4 |  0 0  0  0  2  2 |  *  *  * *  *  * 48  * | 0  0  0  1  0 0  1 1 | 0  1 1 1
... ... ... .xo .ox&#x    0  4 |  0  0 2  4 |  0 0  0  0  0  4 |  *  *  * *  *  *  * 12 | 0  0  0  0  1 0  0 2 | 0  0 2 1
-------------------------+------+------------+------------------+------------------------+----------------------+---------
ox.3oo.3oo. ... ...&#x &  1  4 |  4  6 0  0 |  6 0  0  4  0  0 |  4  0  0 1  0  0  0  0 | 4  *  *  *  * *  * * | 2  0 0 0
oxo3ooo ... ... ...&#x &  1  4 |  4  3 0  3 |  3 0  3  1  3  0 |  1  3  0 0  1  0  0  0 | * 32  *  *  * *  * * | 1  1 0 0
oxo ... oox ... ...&#x    1  4 |  4  2 0  4 |  2 0  4  0  4  0 |  0  4  0 0  0  1  0  0 | *  * 24  *  * *  * * | 1  0 1 0
oxo ... ... ... oox&#x &  1  4 |  4  1 1  4 |  1 1  4  0  2  2 |  0  2  2 0  0  0  1  0 | *  *  * 48  * *  * * | 0  1 1 0
... ... ... oxo oox&#x    1  4 |  4  0 2  4 |  0 2  4  0  0  4 |  0  0  4 0  0  0  0  1 | *  *  *  * 12 *  * * | 0  0 2 0
.xo3.oo3.ox ... ...&#x    0  8 |  0 12 0 12 |  0 0  0  8 24  0 |  0  0  0 2  8  6  0  0 | *  *  *  *  * 4  * * | 1  0 0 1
.xo3.oo ... ... .ox&#x &  0  5 |  0  3 1  6 |  0 0  0  1  6  3 |  0  0  0 0  2  0  3  0 | *  *  *  *  * * 16 * | 0  1 0 1
.xo ... .ox .xo .ox&#zx   0  8 |  0  4 4 16 |  0 0  0  0 16 16 |  0  0  0 0  0  4  8  4 | *  *  *  *  * *  * 6 | 0  0 1 1
-------------------------+------+------------+------------------+------------------------+----------------------+---------
oxo3ooo3oox ... ...&#x    1  8 |  8 12 0 12 | 12 0 12  8 24  0 |  8 24  0 2  8  6  0  0 | 2  8  6  0  0 1  0 0 | 4  * * *
oxo3ooo ... ... oox&#x &  1  5 |  5  3 1  6 |  3 1  6  1  6  3 |  1  6  3 0  2  0  3  0 | 0  2  0  3  0 0  1 0 | * 16 * *
oxo ... oox oxo oox&#x    1  8 |  8  4 4 16 |  4 4 16  0 16 16 |  0 16 16 0  0  4  8  4 | 0  0  4  8  4 0  0 1 | *  * 6 *
.xo3.oo3.ox .xo .ox&#zx   0 16 |  0 24 8 48 |  0 0  0 16 96 48 |  0  0  0 4 32 24 48 12 | 0  0  0  0  0 4 16 6 | *  * * 1

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