Acronym endjak
Name ennea-diminished jak
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art 
    A    	
         	where:
    C    	A = x3o o3o
A       A	C = o3x o3x (triddip)

    A    	where:
B       B	A = x3o o3o ({3})
         	B = o3o x3o (perp {3})
A       A
    B
Face vector 18, 90, 192, 213, 126, 33
Confer
uniform relative:
jak  
related segmentopeta:
trippete  
general polytopal classes:
scaliform  
External
links 		polytopewiki  

Incidence matrix according to Dynkin symbol

xo3ox xo3oo ox3oo&#zx   → height = 0
(tegum sum of 2 perp-dual triddips)

o.3o. o.3o. o.3o.    & | 18 |  2  2  6 | 1  4 1  9  18 | 2 3 15 12  8 12 |  9 18  5 10 | 6  7 2
-----------------------+----+----------+---------------+-----------------+-------------+-------
x. .. .. .. .. ..    & |  2 | 18  *  * | 1  2 0  3   0 | 2 3  6  3  0  0 |  9  6  1  0 | 6  2 0
.. .. x. .. .. ..    & |  2 |  * 18  * | 0  2 1  0   6 | 1 0  6  3  6  6 |  3  9  3  8 | 3  5 2
oo3oo oo3oo oo3oo&#x   |  2 |  *  * 54 | 0  0 0  2   4 | 0 1  4  4  2  4 |  4  8  2  4 | 4  4 1
-----------------------+----+----------+---------------+-----------------+-------------+-------
x.3o. .. .. .. ..    & |  3 |  3  0  0 | 6  * *  *   * ♦ 2 3  0  0  0  0 |  9  0  0  0 | 6  0 0
x. .. x. .. .. ..    & |  4 |  2  2  0 | * 18 *  *   * | 1 0  3  0  0  0 |  3  3  0  0 | 3  1 0
.. .. x.3o. .. ..    & |  3 |  0  3  0 | *  * 6  *   * ♦ 0 0  0  0  6  0 |  0  0  3  6 | 0  3 2
xo .. .. .. .. ..&#x & |  3 |  1  0  2 | *  * * 54   * | 0 1  2  2  0  0 |  4  4  1  0 | 4  2 0
.. .. xo .. .. ..&#x & |  3 |  0  1  2 | *  * *  * 108 | 0 0  1  1  1  2 |  1  4  1  3 | 2  3 1
-----------------------+----+----------+---------------+-----------------+-------------+-------
x.3o. x. .. .. ..    & ♦  6 |  6  3  0 | 2  3 0  0   0 | 6 *  *  *  *  * |  3  0  0  0 | 3  0 0
xo3ox .. .. .. ..&#x   ♦  6 |  6  0  6 | 2  0 0  6   0 | * 9  *  *  *  * |  4  0  0  0 | 4  0 0
xo .. xo .. .. ..&#x & ♦  5 |  2  2  4 | 0  1 0  2   2 | * * 54  *  *  * |  1  2  0  0 | 2  1 0
xo .. .. .. ox ..&#x & ♦  4 |  1  1  4 | 0  0 0  2   2 | * *  * 54  *  * |  1  2  1  0 | 2  2 0
.. .. xo3oo .. ..&#x & ♦  4 |  0  3  3 | 0  0 1  0   3 | * *  *  * 36  * |  0  0  1  2 | 0  2 1
.. .. xo .. ox ..&#x   ♦  4 |  0  2  4 | 0  0 0  0   4 | * *  *  *  * 54 |  0  2  0  2 | 1  2 1
-----------------------+----+----------+---------------+-----------------+-------------+-------
xo3ox xo .. .. ..&#x & ♦  9 |  9  3 12 | 3  3 0 12   6 | 1 2  3  3  0  0 | 18  *  *  * | 2  0 0
xo .. xo .. ox ..&#x & ♦  6 |  2  3  8 | 0  1 0  4   8 | 0 0  2  2  0  2 |  * 54  *  * | 1  1 0
xo .. .. .. ox3oo&#x & ♦  5 |  1  3  6 | 0  0 1  3   6 | 0 0  0  3  2  0 |  *  * 18  * | 0  2 0
.. .. xo3oo ox ..&#x & ♦  5 |  0  4  6 | 0  0 1  0   9 | 0 0  0  0  2  3 |  *  *  * 36 | 0  1 1
-----------------------+----+----------+---------------+-----------------+-------------+-------
xo3ox xo .. ox ..&#x   ♦ 12 | 12  6 24 | 4  6 0 24  24 | 2 4 12 12  0  6 |  4  6  0  0 | 9  * *
xo .. xo .. ox3oo&#x & ♦  7 |  2  5 12 | 0  1 1  6  18 | 0 0  3  6  4  6 |  0  3  2  2 | * 18 *
.. .. xo3oo ox3oo&#x   ♦  6 |  0  6  9 | 0  0 2  0  18 | 0 0  0  0  6  9 |  0  0  0  6 | *  * 6


oxxo oxox3oooo oooo3xoxo&#xt   → height(1,2) = height(3,4) = 1/sqrt(12) = 0.288675
                                 height(2,3) = 1/sqrt(3) = 0.577350
({3} || perp trip || para trip || perp {3})

o... o...3o... o...3o...     & | 6  * | 2  6  2 0  0  0 | 1  3  6 12  6 1  4 0 0  0 |  3  6  2 12  6 3  6 12 2  0  0 |  6 3  4  6  9  2 12  0 | 3 2 6  4 0
.o.. .o..3.o.. .o..3.o..     & | * 12 | 0  3  1 1  2  3 | 0  3  6  3  6 1  2 2 1  9 |  6  3  3  6  1 3  9  9 2  4  6 |  6 1  3  2  9  4 12  5 | 2 1 6  5 1
-------------------------------+------+-----------------+---------------------------+--------------------------------+------------------------+-----------
.... .... .... .... x...     & | 2  0 | 6  *  * *  *  * | 1  0  0  6  0 0  2 0 0  0 |  0  3  0  6  6 0  0  6 1  0  0 |  3 3  2  6  3  0  6  0 | 3 2 3  2 0
oo.. oo..3oo.. oo..3oo..&#x  & | 1  1 | * 36  * *  *  * | 0  1  2  2  1 0  0 0 0  0 |  2  2  1  4  1 1  2  2 0  0  0 |  4 1  2  2  4  1  4  0 | 2 1 4  2 0
o.o. o.o.3o.o. o.o.3o.o.&#x  & | 1  1 | *  * 12 *  *  * | 0  0  0  0  3 1  2 0 0  0 |  0  0  0  0  0 3  3  6 2  0  0 |  0 0  0  0  9  1  6  0 | 0 0 6  2 0
.x.. .... .... .... ....     & | 0  2 | *  *  * 6  *  * | 0  3  0  0  0 1  0 2 0  0 |  6  3  0  0  0 3  0  0 2  0  0 |  6 1  0  0  9  0  0  0 | 2 0 6  0 0
.... .x.. .... .... ....     & | 0  2 | *  *  * * 12  * | 0  0  3  0  0 0  1 1 1  3 |  3  0  3  3  0 0  3  3 1  3  3 |  3 0  3  1  3  3  3  4 | 1 1 3  4 1
.oo. .oo.3.oo. .oo.3.oo.&#x    | 0  2 | *  *  * *  * 18 | 0  0  0  0  2 0  0 0 0  4 |  0  0  0  0  0 1  4  4 0  2  4 |  0 0  0  0  4  2  8  4 | 0 0 4  4 1
-------------------------------+------+-----------------+---------------------------+--------------------------------+------------------------+-----------
.... .... .... o...3x...     & | 3  0 | 3  0  0 0  0  0 | 2  *  *  *  * *  * * *  * ♦  0  0  0  0  6 0  0  0 0  0  0 |  0 3  0  6  0  0  0  0 | 3 2 0  0 0
ox.. .... .... .... ....&#x  & | 1  2 | 0  2  0 1  0  0 | * 18  *  *  * *  * * *  * |  2  2  0  0  0 1  0  0 0  0  0 |  4 1  0  0  4  0  0  0 | 2 0 4  0 0
.... ox.. .... .... ....&#x  & | 1  2 | 0  2  0 0  1  0 | *  * 36  *  * *  * * *  * |  1  0  1  2  0 0  1  0 0  0  0 |  2 0  2  1  1  1  2  0 | 1 1 2  2 0
.... .... .... .... xo..&#x  & | 2  1 | 1  2  0 0  0  0 | *  *  * 36  * *  * * *  * |  0  1  0  2  1 0  0  1 0  0  0 |  2 1  1  2  1  0  2  0 | 2 1 2  1 0
ooo. ooo.3ooo. ooo.3ooo.&#x  & | 1  2 | 0  1  1 0  0  1 | *  *  *  * 36 *  * * *  * |  0  0  0  0  0 1  2  2 0  0  0 |  0 0  0  0  4  1  4  0 | 0 0 4  2 0
o.x. .... .... .... ....&#x  & | 1  2 | 0  0  2 1  0  0 | *  *  *  *  * 6  * * *  * ♦  0  0  0  0  0 3  0  0 2  0  0 |  0 0  0  0  9  0  0  0 | 0 0 6  0 0
.... .... .... .... x.x.&#x  & | 2  2 | 1  0  2 0  1  0 | *  *  *  *  * * 12 * *  * |  0  0  0  0  0 0  0  3 1  0  0 |  0 0  0  0  3  0  3  0 | 0 0 3  1 0
.x.. .x.. .... .... ....     & | 0  4 | 0  0  0 2  2  0 | *  *  *  *  * *  * 6 *  * |  3  0  0  0  0 0  0  0 1  0  0 |  3 0  0  0  3  0  0  0 | 1 0 3  0 0
.... .x..3.o.. .... ....     & | 0  3 | 0  0  0 0  3  0 | *  *  *  *  * *  * * 4  * ♦  0  0  3  0  0 0  0  0 0  3  0 |  0 0  3  0  0  3  0  3 | 0 1 0  3 1
.... .xo. .... .... ....&#x  & | 0  3 | 0  0  0 0  1  2 | *  *  *  *  * *  * * * 36 |  0  0  0  0  0 0  1  1 0  1  2 |  0 0  0  0  1  1  4  3 | 0 0 2  3 1
-------------------------------+------+-----------------+---------------------------+--------------------------------+------------------------+-----------
ox.. ox.. .... .... ....&#x  & ♦ 1  4 | 0  4  0 2  2  0 | 0  2  2  0  0 0  0 1 0  0 | 18  *  *  *  * *  *  * *  *  * |  2 0  0  0  1  0  0  0 | 1 0 2  0 0
ox.. .... .... .... xo..&#x  & ♦ 2  2 | 1  4  0 1  0  0 | 0  2  0  2  0 0  0 0 0  0 |  * 18  *  *  * *  *  * *  *  * |  2 1  0  0  1  0  0  0 | 2 0 2  0 0
.... ox..3oo.. .... ....&#x  & ♦ 1  3 | 0  3  0 0  3  0 | 0  0  3  0  0 0  0 0 1  0 |  *  * 12  *  * *  *  * *  *  * |  0 0  2  0  0  1  0  0 | 0 1 0  2 0
.... ox.. .... .... xo..&#x  & ♦ 2  2 | 1  4  0 0  1  0 | 0  0  2  2  0 0  0 0 0  0 |  *  *  * 36  * *  *  * *  *  * |  1 0  1  1  0  0  1  0 | 1 1 1  1 0
.... .... .... oo..3xo..&#x  & ♦ 3  1 | 3  3  0 0  0  0 | 1  0  0  3  0 0  0 0 0  0 |  *  *  *  * 12 *  *  * *  *  * |  0 1  0  2  0  0  0  0 | 2 1 0  0 0
oxxo .... .... .... ....&#xr   ♦ 2  4 | 0  4  4 2  0  2 | 0  2  0  0  4 2  0 0 0  0 |  *  *  *  *  * 9  *  * *  *  * |  0 0  0  0  4  0  0  0 | 0 0 4  0 0  cycle (ABDC)
.... oxo. .... .... ....&#x  & ♦ 1  3 | 0  2  1 0  1  2 | 0  0  1  0  2 0  0 0 0  1 |  *  *  *  *  * * 36  * *  *  * |  0 0  0  0  1  1  2  0 | 0 0 2  2 0
.... .... .... .... xox.&#x  & ♦ 2  3 | 1  2  2 0  1  2 | 0  0  0  1  2 0  1 0 0  1 |  *  *  *  *  * *  * 36 *  *  * |  0 0  0  0  1  0  2  0 | 0 0 2  1 0
o.x. .... .... .... x.x.&#x  & ♦ 2  4 | 1  0  4 2  2  0 | 0  0  0  0  0 2  2 1 0  0 |  *  *  *  *  * *  *  * 6  *  * |  0 0  0  0  3  0  0  0 | 0 0 3  0 0
.... .xo.3.oo. .... ....&#x  & ♦ 0  4 | 0  0  0 0  3  3 | 0  0  0  0  0 0  0 0 1  3 |  *  *  *  *  * *  *  * * 12  * |  0 0  0  0  0  1  0  2 | 0 0 0  2 1
.... .xo. .... .... .ox.&#x    ♦ 0  4 | 0  0  0 0  2  4 | 0  0  0  0  0 0  0 0 0  4 |  *  *  *  *  * *  *  * *  * 18 |  0 0  0  0  0  0  2  2 | 0 0 1  2 1
-------------------------------+------+-----------------+---------------------------+--------------------------------+------------------------+-----------
ox.. ox.. .... .... xo..&#x  & ♦ 2  4 | 1  8  0 2  2  0 | 0  4  4  4  0 0  0 1 0  0 |  2  2  0  2  0 0  0  0 0  0  0 | 18 *  *  *  *  *  *  * | 1 0 1  0 0
ox.. .... .... oo..3xo..&#x  & ♦ 3  2 | 3  6  0 1  0  0 | 1  3  0  6  0 0  0 0 0  0 |  0  3  0  0  2 0  0  0 0  0  0 |  * 6  *  *  *  *  *  * | 2 0 0  0 0
.... ox..3oo.. .... xo..&#x  & ♦ 2  3 | 1  6  0 0  3  0 | 0  0  6  3  0 0  0 0 1  0 |  0  0  2  3  0 0  0  0 0  0  0 |  * * 12  *  *  *  *  * | 0 1 0  1 0
.... ox.. .... oo..3xo..&#x  & ♦ 3  2 | 3  6  0 0  1  0 | 1  0  3  6  0 0  0 0 0  0 |  0  0  0  3  2 0  0  0 0  0  0 |  * *  * 12  *  *  *  * | 1 1 0  0 0
oxxo oxox .... .... ....&#xr & ♦ 3  6 | 1  8  6 3  2  4 | 0  4  2  2  8 3  2 1 0  2 |  1  1  0  0  0 2  2  2 1  0  0 |  * *  *  * 18  *  *  * | 0 0 2  0 0  cycle (ABDC)
.... oxo.3ooo. .... ....&#x  & ♦ 1  4 | 0  3  1 0  3  3 | 0  0  3  0  3 0  0 0 1  3 |  0  0  1  0  0 0  3  0 0  1  0 |  * *  *  *  * 12  *  * | 0 0 0  2 0
.... oxo. .... .... xox.&#x  & ♦ 2  4 | 1  4  2 0  1  4 | 0  0  2  2  4 0  1 0 0  4 |  0  0  0  1  0 0  2  2 0  0  1 |  * *  *  *  *  * 36  * | 0 0 1  1 0
.... .xo.3.oo. .... .ox.&#x  & ♦ 0  5 | 0  0  0 0  4  6 | 0  0  0  0  0 0  0 0 1  9 |  0  0  0  0  0 0  0  0 0  2  3 |  * *  *  *  *  *  * 12 | 0 0 0  1 1
-------------------------------+------+-----------------+---------------------------+--------------------------------+------------------------+-----------
ox.. ox.. .... oo..3xo..&#x  & ♦ 3  4 | 3 12  0 2  2  0 | 1  6  6 12  0 0  0 1 0  0 |  3  6  0  6  4 0  0  0 0  0  0 |  3 2  0  2  0  0  0  0 | 6 * *  * *
.... ox..3oo.. oo..3xo..&#x  & ♦ 3  3 | 3  9  0 0  3  0 | 1  0  9  9  0 0  0 0 1  0 |  0  0  3  9  3 0  0  0 0  0  0 |  0 0  3  3  0  0  0  0 | * 4 *  * *
oxxo oxox .... .... xoxo&#xr   ♦ 4  8 | 2 16  8 4  4  8 | 0  8  8  8 16 4  4 2 0  8 |  4  4  0  4  0 4  8  8 2  0  2 |  2 0  0  0  4  0  4  0 | * * 9  * *  cycle (ABDC)
.... oxo.3ooo. .... xox.&#x  & ♦ 2  5 | 1  6  2 0  4  6 | 0  0  6  3  6 0  1 0 1  9 |  0  0  2  3  0 0  6  3 0  2  3 |  0 0  1  0  0  2  3  1 | * * * 12 *
.... .xo.3.oo. .oo.3.ox.&#x  & ♦ 0  6 | 0  0  0 0  6  9 | 0  0  0  0  0 0  0 0 2 18 |  0  0  0  0  0 0  0  0 0  6  9 |  0 0  0  0  0  0  0  6 | * * *  * 2

© 2004-2025
top of page