Acronym trathiddip
Name triangle atop thiddip,
triangle-first cap of sarx
Circumradius sqrt(5/3) = 1.290994
Lace hyper city
in approx. ASCII-art
       x3o    
        x3x   
x3x           
           x3x
(shallow triangular pyramid with {3} at the tip and {6} at the base vertices)
Confer
uniform relative:
sarx  
general polytopal classes:
segmentotera  

This polyteron can be seen as triangle-first cap of sarx when the latter is being presented within axial A2×A2 subsymmetry.


Incidence matrix according to Dynkin symbol

oo3ox ox3xx&#x   → height = 1/sqrt(3) = 0.577350
({3} || thiddip)

o.3o. o.3o.    | 3  * | 2  6  0 0 0 | 1  6 3 6 0 0 0 0 | 2 3 6 3 0 0 0 | 1 2 3 0
.o3.o .o3.o    | * 18 | 0  1  2 1 1 | 0  2 1 1 1 2 2 1 | 1 2 2 1 1 1 2 | 1 1 2 1
---------------+------+-------------+------------------+---------------+--------
.. .. .. x.    | 2  0 | 3  *  * * * | 1  0 0 3 0 0 0 0 | 0 0 3 3 0 0 0 | 0 1 3 0
oo3oo oo3oo&#x | 1  1 | * 18  * * * | 0  2 1 1 0 0 0 0 | 1 2 2 1 0 0 0 | 1 1 2 0
.. .x .. ..    | 0  2 | *  * 18 * * | 0  1 0 0 1 1 1 0 | 1 1 1 0 1 1 1 | 1 1 1 1
.. .. .x ..    | 0  2 | *  *  * 9 * | 0  0 1 0 0 2 0 1 | 0 2 0 1 1 0 2 | 1 0 2 1
.. .. .. .x    | 0  2 | *  *  * * 9 | 0  0 0 1 0 0 2 1 | 0 0 2 1 0 1 2 | 0 1 2 1
---------------+------+-------------+------------------+---------------+--------
.. .. o.3x.    | 3  0 | 3  0  0 0 0 | 1  * * * * * * * | 0 0 0 3 0 0 0 | 0 0 3 0
.. ox .. ..&#x | 1  2 | 0  2  1 0 0 | * 18 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
.. .. ox ..&#x | 1  2 | 0  2  0 1 0 | *  * 9 * * * * * | 0 2 0 1 0 0 0 | 1 0 2 0
.. .. .. xx&#x | 2  2 | 1  2  0 0 1 | *  * * 9 * * * * | 0 0 2 1 0 0 0 | 0 1 2 0
.o3.x .. ..    | 0  3 | 0  0  3 0 0 | *  * * * 6 * * * | 1 0 0 0 1 1 0 | 1 1 0 1
.. .x .x ..    | 0  4 | 0  0  2 2 0 | *  * * * * 9 * * | 0 1 0 0 1 0 1 | 1 0 1 1
.. .x .. .x    | 0  4 | 0  0  2 0 2 | *  * * * * * 9 * | 0 0 1 0 0 1 1 | 0 1 1 1
.. .. .x3.x    | 0  6 | 0  0  0 3 3 | *  * * * * * * 3 | 0 0 0 1 0 0 2 | 0 0 2 1
---------------+------+-------------+------------------+---------------+--------
oo3ox .. ..&#x  1  3 | 0  3  3 0 0 | 0  3 0 0 1 0 0 0 | 6 * * * * * * | 1 1 0 0
.. ox ox ..&#x  1  4 | 0  4  2 2 0 | 0  2 2 0 0 1 0 0 | * 9 * * * * * | 1 0 1 0
.. ox .. xx&#x  2  4 | 1  4  2 0 2 | 0  2 0 2 0 0 1 0 | * * 9 * * * * | 0 1 1 0
.. .. ox3xx&#x  3  6 | 3  6  0 3 3 | 1  0 3 3 0 0 0 1 | * * * 3 * * * | 0 0 2 0
.o3.x .x ..     0  6 | 0  0  6 3 0 | 0  0 0 0 2 3 0 0 | * * * * 3 * * | 1 0 0 1
.o3.x .. .x     0  6 | 0  0  6 0 3 | 0  0 0 0 2 0 3 0 | * * * * * 3 * | 0 1 0 1
.. .x .x3.x     0 12 | 0  0  6 6 6 | 0  0 0 0 0 3 3 2 | * * * * * * 3 | 0 0 1 1
---------------+------+-------------+------------------+---------------+--------
oo3ox ox ..&#x  1  6 | 0  6  6 3 0 | 0  6 3 0 2 3 0 0 | 2 3 0 0 1 0 0 | 3 * * *
oo3ox .. xx&#x  2  6 | 1  6  6 0 3 | 0  6 0 3 2 0 3 0 | 2 0 3 0 0 1 0 | * 3 * *
.. ox ox3xx&#x  3 12 | 3 12  6 6 6 | 1  6 6 6 0 3 3 2 | 0 3 3 2 0 0 1 | * * 3 *
.o3.x .x3.x     0 18 | 0  0 18 9 9 | 0  0 0 0 6 9 9 3 | 0 0 0 0 3 3 3 | * * * 1

oxxx3xxxx&#x   → height(1,2) = height(1,3) = height(1,4) = sqrt(2/3) = 0.816497
                 height(2,3) = height(2,4) = height(3,4) = 1

o...3o...    | 3 * * * | 2 2 2 2 0 0 0 0 0 0 0 0 0 | 1 1 2 2 2 1 2 2 1 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 2 1 2 1 1 2 1 0 0 0 0 0 | 1 1 1 1 1 0
.o..3.o..    | * 6 * * | 0 1 0 0 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 | 1 1 1 1 0 1
..o.3..o.    | * * 6 * | 0 0 1 0 0 0 1 0 1 1 1 0 0 | 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 | 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 | 1 1 1 0 1 1
...o3...o    | * * * 6 | 0 0 0 1 0 0 0 1 0 0 1 1 1 | 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 | 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
-------------+---------+---------------------------+-----------------------------------------+-------------------------------+------------
.... x...    | 2 0 0 0 | 3 * * * * * * * * * * * * | 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 | 1 0 1 1 1 0
oo..3oo..&#x | 1 1 0 0 | * 6 * * * * * * * * * * * | 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0
o.o.3o.o.&#x | 1 0 1 0 | * * 6 * * * * * * * * * * | 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 1 0
o..o3o..o&#x | 1 0 0 1 | * * * 6 * * * * * * * * * | 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x.. ....    | 0 2 0 0 | * * * * 3 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
.... .x..    | 0 2 0 0 | * * * * * 3 * * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 | 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo.3.oo.&#x | 0 1 1 0 | * * * * * * 6 * * * * * * | 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
.o.o3.o.o&#x | 0 1 0 1 | * * * * * * * 6 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x. ....    | 0 0 2 0 | * * * * * * * * 3 * * * * | 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 | 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 | 1 1 0 0 1 1
.... ..x.    | 0 0 2 0 | * * * * * * * * * 3 * * * | 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 | 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 | 1 0 1 0 1 1
..oo3..oo&#x | 0 0 1 1 | * * * * * * * * * * 6 * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
...x ....    | 0 0 0 2 | * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 | 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
.... ...x    | 0 0 0 2 | * * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 | 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
-------------+---------+---------------------------+-----------------------------------------+-------------------------------+------------
o...3x...    | 3 0 0 0 | 3 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
ox.. ....&#x | 1 2 0 0 | 0 2 0 0 1 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
.... xx..&#x | 2 2 0 0 | 1 2 0 0 0 1 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo.3ooo.&#x | 1 1 1 0 | 0 1 1 0 0 0 1 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo.o3oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 0 1 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x. ....&#x | 1 0 2 0 | 0 0 2 0 0 0 0 0 1 0 0 0 0 | * * * * * 3 * * * * * * * * * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
.... x.x.&#x | 2 0 2 0 | 1 0 2 0 0 0 0 0 0 1 0 0 0 | * * * * * * 3 * * * * * * * * * * * * * | 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
o.oo3o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 0 0 1 0 0 | * * * * * * * 6 * * * * * * * * * * * * | 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
o..x ....&#x | 1 0 0 2 | 0 0 0 2 0 0 0 0 0 0 0 1 0 | * * * * * * * * 3 * * * * * * * * * * * | 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
.... x..x&#x | 2 0 0 2 | 1 0 0 2 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 3 * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x..3.x..    | 0 6 0 0 | 0 0 0 0 3 3 0 0 0 0 0 0 0 | * * * * * * * * * * 1 * * * * * * * * * | 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx. ....&#x | 0 2 2 0 | 0 0 0 0 1 0 2 0 1 0 0 0 0 | * * * * * * * * * * * 3 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.... .xx.&#x | 0 2 2 0 | 0 0 0 0 0 1 2 0 0 1 0 0 0 | * * * * * * * * * * * * 3 * * * * * * * | 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 0 0 1 1 0 0 1 0 0 | * * * * * * * * * * * * * 6 * * * * * * | 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.x.x ....&#x | 0 2 0 2 | 0 0 0 0 1 0 0 2 0 0 0 1 0 | * * * * * * * * * * * * * * 3 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
.... .x.x&#x | 0 2 0 2 | 0 0 0 0 0 1 0 2 0 0 0 0 1 | * * * * * * * * * * * * * * * 3 * * * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x.3..x.    | 0 0 6 0 | 0 0 0 0 0 0 0 0 3 3 0 0 0 | * * * * * * * * * * * * * * * * 1 * * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1
..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 0 0 0 1 0 2 1 0 | * * * * * * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
.... ..xx&#x | 0 0 2 2 | 0 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
...x3...x    | 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
-------------+---------+---------------------------+-----------------------------------------+-------------------------------+------------
ox..3xx..&#x  3 6 0 0 | 3 6 0 0 3 3 0 0 0 0 0 0 0 | 1 3 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * | 1 0 0 1 0 0
oxx. ....&#x  1 2 2 0 | 0 2 2 0 1 0 2 0 1 0 0 0 0 | 0 1 0 2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * | 1 1 0 0 0 0
.... xxx.&#x  2 2 2 0 | 1 2 2 0 0 1 2 0 0 1 0 0 0 | 0 0 1 2 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * | 1 0 1 0 0 0
oooo3oooo&#x  1 1 1 1 | 0 1 1 1 0 0 1 1 0 0 1 0 0 | 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 | * * * 6 * * * * * * * * * * * | 0 1 1 0 0 0
ox.x ....&#x  1 2 0 2 | 0 2 0 2 1 0 0 2 0 0 0 1 0 | 0 1 0 0 2 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 | * * * * 3 * * * * * * * * * * | 0 1 0 1 0 0
.... xx.x&#x  2 2 0 2 | 1 2 0 2 0 1 0 2 0 0 0 0 1 | 0 0 1 0 2 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 | * * * * * 3 * * * * * * * * * | 0 0 1 1 0 0
o.x.3x.x.&#x  3 0 6 0 | 3 0 6 0 0 0 0 0 3 3 0 0 0 | 1 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 1 0 0 0 | * * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
o.xx ....&#x  1 0 2 2 | 0 0 2 2 0 0 0 0 1 0 2 1 0 | 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 1 0 0 | * * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
.... x.xx&#x  2 0 2 2 | 1 0 2 2 0 0 0 0 0 1 2 0 1 | 0 0 0 0 0 0 1 2 0 1 0 0 0 0 0 0 0 0 1 0 | * * * * * * * * 3 * * * * * * | 0 0 1 0 1 0
o..x3x..x&#x  3 0 0 6 | 3 0 0 6 0 0 0 0 0 0 0 3 3 | 1 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 1 | * * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
.xx.3.xx.&#x  0 6 6 0 | 0 0 0 0 3 3 6 0 3 3 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 3 3 0 0 0 1 0 0 0 | * * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xxx ....&#x  0 2 2 2 | 0 0 0 0 1 0 2 2 1 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 1 0 0 | * * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.... .xxx&#x  0 2 2 2 | 0 0 0 0 0 1 2 2 0 1 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1 0 0 1 0 | * * * * * * * * * * * * 3 * * | 0 0 1 0 0 1
.x.x3.x.x&#x  0 6 0 6 | 0 0 0 0 3 3 0 6 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 3 0 0 0 1 | * * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..xx3..xx&#x  0 0 6 6 | 0 0 0 0 0 0 0 0 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 | * * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+---------------------------+-----------------------------------------+-------------------------------+------------
oxx.3xxx.&#x  3 6 6 0 | 3 6 6 0 3 3 6 0 3 3 0 0 0 | 1 3 3 6 0 3 3 0 0 0 1 3 3 0 0 0 1 0 0 0 | 1 3 3 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
oxxx ....&#x  1 2 2 2 | 0 2 2 2 1 0 2 2 1 0 2 1 0 | 0 1 0 2 2 1 0 2 1 0 0 1 0 2 1 0 0 1 0 0 | 0 1 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 3 * * * *
.... xxxx&#x  2 2 2 2 | 1 2 2 2 0 1 2 2 0 1 2 0 1 | 0 0 1 2 2 0 1 2 0 1 0 0 1 2 0 1 0 0 1 0 | 0 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 3 * * *
ox.x3xx.x&#x  3 6 0 6 | 3 6 0 6 3 3 0 6 0 0 0 3 3 | 1 3 3 0 6 0 0 0 3 3 1 0 0 0 3 3 0 0 0 1 | 1 0 0 0 3 3 0 0 0 1 0 0 0 1 0 | * * * 1 * *
o.xx3x.xx&#x  3 0 6 6 | 3 0 6 6 0 0 0 0 3 3 6 3 3 | 1 0 0 0 0 3 3 6 3 3 0 0 0 0 0 0 1 3 3 1 | 0 0 0 0 0 0 1 3 3 1 0 0 0 0 1 | * * * * 1 *
.xxx3.xxx&#x  0 6 6 6 | 0 0 0 0 3 3 6 6 3 3 6 3 3 | 0 0 0 0 0 0 0 0 0 0 1 3 3 6 3 3 1 3 3 1 | 0 0 0 0 0 0 0 0 0 0 1 3 3 1 1 | * * * * * 1

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