Acronym tripal triddip
Name trip atop gyro-perp triddip
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art
A       A
    B    

where:
A = o3x o3o ({3})
B = x3o x3o (triddip)
Lace hyper city
in approx. ASCII-art
    e    
         
         
e       e
         
         
t       t
         
         
    t    
where:
e = x o3o
t = o x3o
Confer
uniform relative:
jak  
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

xo ox3xo ox3oo&#x   → height = 1/sqrt(12) = 0.288675
(trip || gyro-perp triddip)

o. o.3o. o.3o.    | 6 * | 1 2  6 0 0 | 2 1  6  3  6  6 0 0 0 | 1 3 6  6 3  3  6  2 0 0 | 3 3 6 2 3 1 2 0 | 3 1 2 1
.o .o3.o .o3.o    | * 9 | 0 0  4 2 2 | 0 0  2  4  2  8 1 4 1 | 0 2 1  4 2  8  4  4 2 2 | 1 4 2 2 4 4 2 1 | 2 2 1 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x. .. .. .. ..    | 2 0 | 3 *  * * * | 2 0  6  0  0  0 0 0 0 | 1 3 6  6 0  0  0  0 0 0 | 3 3 6 2 0 0 0 0 | 3 1 2 0
.. .. x. .. ..    | 2 0 | * 6  * * * | 1 1  0  0  3  0 0 0 0 | 1 0 3  0 3  0  3  0 0 0 | 3 0 3 0 3 0 1 0 | 3 0 1 1
oo oo3oo oo3oo&#x | 1 1 | * * 36 * * | 0 0  1  1  1  2 0 0 0 | 0 1 1  2 1  2  2  1 0 0 | 1 2 2 1 2 1 1 0 | 2 1 1 1
.. .x .. .. ..    | 0 2 | * *  * 9 * | 0 0  0  2  0  0 1 2 0 | 0 1 0  0 2  4  0  0 2 1 | 1 2 0 0 4 2 0 1 | 2 1 0 2
.. .. .. .x ..    | 0 2 | * *  * * 9 | 0 0  0  0  0  4 0 2 1 | 0 0 0  2 0  4  2  4 1 2 | 0 2 1 2 2 4 2 1 | 1 2 1 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x. .. x. .. ..    | 4 0 | 2 2  0 0 0 | 3 *  *  *  *  * * * * | 1 0 3  0 0  0  0  0 0 0 | 3 0 3 0 0 0 0 0 | 3 0 1 0
.. o.3x. .. ..    | 3 0 | 0 3  0 0 0 | * 2  *  *  *  * * * * | 1 0 0  0 3  0  0  0 0 0 | 3 0 0 0 3 0 0 0 | 3 0 0 1
xo .. .. .. ..&#x | 2 1 | 1 0  2 0 0 | * * 18  *  *  * * * * | 0 1 1  2 0  0  0  0 0 0 | 1 2 2 1 0 0 0 0 | 2 1 1 0
.. ox .. .. ..&#x | 1 2 | 0 0  2 1 0 | * *  * 18  *  * * * * | 0 1 0  0 1  2  0  0 0 0 | 1 2 0 0 2 1 0 0 | 2 1 0 1
.. .. xo .. ..&#x | 2 1 | 0 1  2 0 0 | * *  *  * 18  * * * * | 0 0 1  0 1  0  2  0 0 0 | 1 0 2 0 2 0 1 0 | 2 0 1 1
.. .. .. ox ..&#x | 1 2 | 0 0  2 0 1 | * *  *  *  * 36 * * * | 0 0 0  1 0  1  1  1 0 0 | 0 1 1 1 1 1 1 0 | 1 1 1 1
.. .x3.o .. ..    | 0 3 | 0 0  0 3 0 | * *  *  *  *  * 3 * * | 0 0 0  0 2  0  0  0 2 0 | 1 0 0 0 4 0 0 1 | 2 0 0 2
.. .x .. .x ..    | 0 4 | 0 0  0 2 2 | * *  *  *  *  * * 9 * | 0 0 0  0 0  2  0  0 1 1 | 0 1 0 0 2 2 0 1 | 1 1 0 2
.. .. .. .x3.o    | 0 3 | 0 0  0 0 3 | * *  *  *  *  * * * 3 | 0 0 0  0 0  0  0  4 0 2 | 0 0 0 2 0 4 2 1 | 0 2 1 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x. o.3x. .. ..     6 0 | 3 6  0 0 0 | 3 2  0  0  0  0 0 0 0 | 1 * *  * *  *  *  * * * | 3 0 0 0 0 0 0 0 | 3 0 0 0
xo ox .. .. ..&#x  2 2 | 1 0  4 1 0 | 0 0  2  2  0  0 0 0 0 | * 9 *  * *  *  *  * * * | 1 2 0 0 0 0 0 0 | 2 1 0 0
xo .. xo .. ..&#x  4 1 | 2 2  4 0 0 | 1 0  2  0  2  0 0 0 0 | * * 9  * *  *  *  * * * | 1 0 2 0 0 0 0 0 | 2 0 1 0
xo .. .. ox ..&#x  2 2 | 1 0  4 0 1 | 0 0  2  0  0  2 0 0 0 | * * * 18 *  *  *  * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
.. ox3xo .. ..&#x  3 3 | 0 3  6 3 0 | 0 1  0  3  3  0 1 0 0 | * * *  * 6  *  *  * * * | 1 0 0 0 2 0 0 0 | 2 0 0 1
.. ox .. ox ..&#x  1 4 | 0 0  4 2 2 | 0 0  0  2  0  2 0 1 0 | * * *  * * 18  *  * * * | 0 1 0 0 1 1 0 0 | 1 1 0 1
.. .. xo ox ..&#x  2 2 | 0 1  4 0 1 | 0 0  0  0  2  2 0 0 0 | * * *  * *  * 18  * * * | 0 0 1 0 1 0 1 0 | 1 0 1 1
.. .. .. ox3oo&#x  1 3 | 0 0  3 0 3 | 0 0  0  0  0  3 0 0 1 | * * *  * *  *  * 12 * * | 0 0 0 1 0 1 1 0 | 0 1 1 1
.. .x3.o .x ..     0 6 | 0 0  0 6 3 | 0 0  0  0  0  0 2 3 0 | * * *  * *  *  *  * 3 * | 0 0 0 0 2 0 0 1 | 1 0 0 2
.. .x .. .x3.o     0 6 | 0 0  0 3 6 | 0 0  0  0  0  0 0 3 2 | * * *  * *  *  *  * * 3 | 0 0 0 0 0 2 0 1 | 0 1 0 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
xo ox3xo .. ..&#x  6 3 | 3 6 12 3 0 | 3 2  6  6  6  0 1 0 0 | 1 3 3  0 2  0  0  0 0 0 | 3 * * * * * * * | 2 0 0 0
xo ox .. ox ..&#x  2 4 | 1 0  8 2 2 | 0 0  4  4  0  4 0 1 0 | 0 2 0  2 0  2  0  0 0 0 | * 9 * * * * * * | 1 1 0 0
xo .. xo ox ..&#x  4 2 | 2 2  8 0 1 | 1 0  4  0  4  4 0 0 0 | 0 0 2  2 0  0  2  0 0 0 | * * 9 * * * * * | 1 0 1 0
xo .. .. ox3oo&#x  2 3 | 1 0  6 0 3 | 0 0  3  0  0  6 0 0 1 | 0 0 0  3 0  0  0  2 0 0 | * * * 6 * * * * | 0 1 1 0
.. ox3xo ox ..&#x  3 6 | 0 3 12 6 3 | 0 1  0  6  6  6 2 3 0 | 0 0 0  0 2  3  3  0 1 0 | * * * * 6 * * * | 1 0 0 1
.. ox .. ox3oo&#x  1 6 | 0 0  6 3 6 | 0 0  0  3  0  6 0 3 2 | 0 0 0  0 0  3  0  2 0 1 | * * * * * 6 * * | 0 1 0 1
.. .. xo ox3oo&#x  2 3 | 0 1  6 0 3 | 0 0  0  0  3  6 0 0 1 | 0 0 0  0 0  0  3  2 0 0 | * * * * * * 6 * | 0 0 1 1
.. .x3.o .x3.o     0 9 | 0 0  0 9 9 | 0 0  0  0  0  0 3 9 3 | 0 0 0  0 0  0  0  0 3 3 | * * * * * * * 1 | 0 0 0 2
------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
xo ox3xo ox ..&#x  6 6 | 3 6 24 6 3 | 3 2 12 12 12 12 2 3 0 | 1 6 6  6 4  6  6  0 1 0 | 2 3 3 0 2 0 0 0 | 3 * * *
xo ox .. ox3oo&#x  2 6 | 1 0 12 3 6 | 0 0  6  6  0 12 0 3 2 | 0 3 0  6 0  6  0  4 0 1 | 0 3 0 2 0 2 0 0 | * 3 * *
xo .. xo ox3oo&#x  4 3 | 2 2 12 0 3 | 1 0  6  0  6 12 0 0 1 | 0 0 3  6 0  0  6  4 0 0 | 0 0 3 2 0 0 2 0 | * * 3 *
.. ox3xo ox3oo&#x  3 9 | 0 3 18 9 9 | 0 1  0  9  9 18 3 9 3 | 0 0 0  0 3  9  9  6 3 3 | 0 0 0 0 3 3 3 1 | * * * 2

xoxoxo3oooooo oxoxox&#xr   → all consecutive pairwise heights = sqrt(5/12) = 0.645497
                             all alternating pairwise heights = 1
                             Note: these lengths show that this cycle is not flat, rather it is wobbling up and down!

o.....3o..... o.....     & | 9 * | 2  4 2 0 0 | 1  8  2  4 4 1  2 0 0 |  4  4  8 2 2 2 2  4 1 0 | 2 4 4 4 1 1 2 2 | 2 2 2 1
.o....3.o.... .o....     & | * 6 | 0  6 0 1 2 | 0  6  6  3 0 0  6 2 1 |  2  6  3 3 3 0 0  6 6 1 | 2 1 3 3 3 0 2 6 | 1 1 3 2
---------------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x..... ...... ......     & | 2 0 | 9  * * * * | 1  4  0  0 2 0  0 0 0 |  4  2  4 0 0 2 1  2 0 0 | 2 4 2 2 0 1 2 2 | 2 2 1 1
oo....3oo.... oo....&#x  & | 1 1 | * 36 * * * | 0  2  1  1 0 0  1 0 0 |  1  2  2 1 1 0 0  2 1 0 | 1 1 2 2 1 0 1 2 | 1 1 2 1
o.o...3o.o... o.o...&#x  & | 2 0 | *  * 9 * * | 0  0  0  2 2 1  0 0 0 |  0  0  4 1 2 1 2  0 0 0 | 0 2 2 4 1 1 0 0 | 1 2 2 0
...... ...... .x....     & | 0 2 | *  * * 3 * | 0  0  6  0 0 0  0 2 0 |  0  6  0 3 0 0 0  0 6 1 | 2 0 3 0 3 0 0 6 | 1 0 3 2
.o.o..3.o.o.. .o.o..&#x  & | 0 2 | *  * * * 6 | 0  0  0  0 0 0  3 1 1 |  0  0  0 0 3 0 0  3 3 1 | 0 0 0 3 3 0 1 3 | 0 1 3 1
---------------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
x.....3o..... ......     & | 3 0 | 3  0 0 0 0 | 3  *  *  * * *  * * * |  4  0  0 0 0 2 0  0 0 0 | 2 4 0 0 0 1 2 0 | 2 2 0 1
xo.... ...... ......&#x  & | 2 1 | 1  2 0 0 0 | * 36  *  * * *  * * * |  1  1  1 0 0 0 0  1 0 0 | 1 1 1 1 0 0 1 1 | 1 1 1 1
...... ...... ox....&#x  & | 1 2 | 0  2 0 1 0 | *  * 18  * * *  * * * |  0  2  0 1 0 0 0  0 1 0 | 1 0 2 0 1 0 0 2 | 1 0 2 1
ooo...3ooo... ooo...&#x  & | 2 1 | 0  2 1 0 0 | *  *  * 18 * *  * * * |  0  0  2 1 1 0 0  0 0 0 | 0 1 2 2 1 0 0 0 | 1 1 2 0
x.x... ...... ......&#x  & | 4 0 | 2  0 2 0 0 | *  *  *  * 9 *  * * * |  0  0  2 0 0 1 1  0 0 0 | 0 2 1 2 0 1 0 0 | 1 2 1 0
o.o.o.3o.o.o. o.o.o.&#x    | 3 0 | 0  0 3 0 0 | *  *  *  * * 3  * * * |  0  0  0 0 2 0 2  0 0 0 | 0 0 0 4 1 1 0 0 | 0 2 2 0
.ooo..3.ooo.. .ooo..&#x  & | 1 2 | 0  2 0 0 1 | *  *  *  * * * 18 * * |  0  0  0 0 1 0 0  2 1 0 | 0 0 0 2 1 0 1 2 | 0 1 2 1
...... ...... .x.x..&#x  & | 0 4 | 0  0 0 2 2 | *  *  *  * * *  * 3 * |  0  0  0 0 0 0 0  0 3 1 | 0 0 0 0 3 0 0 3 | 0 0 3 1
.o.o.o3.o.o.o .o.o.o&#x    | 0 3 | 0  0 0 0 3 | *  *  *  * * *  * * 2 |  0  0  0 0 3 0 0  0 0 1 | 0 0 0 3 3 0 0 0 | 0 1 3 0
---------------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
xo....3oo.... ......&#x  &  3 1 | 3  3 0 0 0 | 1  3  0  0 0 0  0 0 0 | 12  *  * * * * *  * * * | 1 1 0 0 0 0 1 0 | 1 1 0 1
xo.... ...... ox....&#x  &  2 2 | 1  4 0 1 0 | 0  2  2  0 0 0  0 0 0 |  * 18  * * * * *  * * * | 1 0 1 0 0 0 0 1 | 1 0 1 1
xox... ...... ......&#x  &  4 1 | 2  4 2 0 0 | 0  2  0  2 1 0  0 0 0 |  *  * 18 * * * *  * * * | 0 1 1 1 0 0 0 0 | 1 1 1 0
...... ...... oxo...&#x  &  2 2 | 0  4 1 1 0 | 0  0  2  2 0 0  0 0 0 |  *  *  * 9 * * *  * * * | 0 0 2 0 1 0 0 0 | 1 0 2 0
oooooo3oooooo oooooo&#xr    3 3 | 0  6 3 0 3 | 0  0  0  3 0 1  3 0 1 |  *  *  * * 6 * *  * * * | 0 0 0 2 1 0 0 0 | 0 1 2 0
x.x...3o.o... ......&#x  &  6 0 | 6  0 3 0 0 | 2  0  0  0 3 0  0 0 0 |  *  *  * * * 3 *  * * * | 0 2 0 0 0 1 0 0 | 1 2 0 0
x.x.x. ...... ......&#x     6 0 | 3  0 6 0 0 | 0  0  0  0 3 2  0 0 0 |  *  *  * * * * 3  * * * | 0 0 0 2 0 1 0 0 | 0 2 1 0
.oxo.. ...... ......&#x  &  2 2 | 1  4 0 0 1 | 0  2  0  0 0 0  2 0 0 |  *  *  * * * * * 18 * * | 0 0 0 1 0 0 1 1 | 0 1 1 1
...... ...... .xox..&#x  &  1 4 | 0  4 0 2 2 | 0  0  2  0 0 0  2 1 0 |  *  *  * * * * *  * 9 * | 0 0 0 0 1 0 0 2 | 0 0 2 1
...... ...... .x.x.x&#x     0 6 | 0  0 0 3 6 | 0  0  0  0 0 0  0 3 2 |  *  *  * * * * *  * * 1 | 0 0 0 0 3 0 0 0 | 0 0 3 0
---------------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
xo....3oo.... ox....&#x  &  3 2 | 3  6 0 1 0 | 1  6  3  0 0 0  0 0 0 |  2  3  0 0 0 0 0  0 0 0 | 6 * * * * * * * | 1 0 0 1
xox...3ooo... ......&#x  &  6 1 | 6  6 3 0 0 | 2  6  0  3 3 0  0 0 0 |  2  0  3 0 0 1 0  0 0 0 | * 6 * * * * * * | 1 1 0 0
xox... ...... oxo...&#x  &  4 2 | 2  8 2 1 0 | 0  4  4  4 1 0  0 0 0 |  0  2  2 2 0 0 0  0 0 0 | * * 9 * * * * * | 1 0 1 0
xoxoxo ...... ......&#xr    6 3 | 3 12 6 0 3 | 0  6  0  6 3 2  6 0 1 |  0  0  3 0 2 0 1  3 0 0 | * * * 6 * * * * | 0 1 1 0
...... ...... oxoxox&#xr    3 6 | 0 12 3 3 6 | 0  0  6  6 0 1  6 3 2 |  0  0  0 3 2 0 0  0 3 1 | * * * * 3 * * * | 0 0 2 0
x.x.x.3o.o.o. ......&#x     9 0 | 9  0 9 0 0 | 3  0  0  0 9 3  0 0 0 |  0  0  0 0 0 3 3  0 0 0 | * * * * * 1 * * | 0 2 0 0
.oxo..3.ooo.. ......&#x  &  3 2 | 3  6 0 0 1 | 1  6  0  0 0 0  3 0 0 |  2  0  0 0 0 0 0  3 0 0 | * * * * * * 6 * | 0 1 0 1
.oxo.. ...... .xox..&#x  &  2 4 | 1  8 0 2 2 | 0  4  4  0 0 0  4 1 0 |  0  2  0 0 0 0 0  2 2 0 | * * * * * * * 9 | 0 0 1 1
---------------------------+-----+------------+-----------------------+-------------------------+-----------------+--------
xox...3ooo... oxo...&#x  &  6 2 | 6 12 3 1 0 | 2 12  6  6 3 0  0 0 0 |  4  6  6 3 0 1 0  0 0 0 | 2 2 3 0 0 0 0 0 | 3 * * *
xoxoxo3oooooo ......&#xr    9 3 | 9 18 9 0 3 | 3 18  0  9 9 3  9 0 1 |  6  0  9 0 3 3 3  9 0 0 | 0 3 0 3 0 1 3 0 | * 2 * *
xoxoxo ...... oxoxox&#xr    6 6 | 3 24 6 3 6 | 0 12 12 12 3 2 12 3 2 |  0  6  6 6 4 0 1  6 6 1 | 0 0 3 2 2 0 0 3 | * * 3 *
.oxo..3.ooo.. .xox..&#x  &  3 4 | 3 12 0 2 2 | 1 12  6  0 0 0  6 1 0 |  4  6  0 0 0 0 0  6 3 0 | 2 0 0 0 0 0 2 3 | * * * 3

© 2004-2021
top of page