Acronym squasquasc
Name {4} atop squasc
Circumradius sqrt(5/8) = 0.790569
Lace hyper city
in approx. ASCII-art
o x             
             o x
                
            x x 
                
  x o           
(disphenoid in configuration space)
         
         
   x x   
         
         
x o   o x
         
         
         
o x      
({4} || squasc)
Confer
uniform relative:
hin  
related segmentotera:
dihin   bidhin   tedhin  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

ooxx xxox&#x   → height(1,2) = 1
                 height(1,3) = height(2,3) = sqrt(2/3) = 0.816497
                 height(1,4) = height(2,4) = height(3,4) = sqrt(3)/2 = 0.866025
                 height(123,4) = 1/sqrt(2) = 0.707107 ({4} || squasc)

o... o...    | 2 * * * | 1 1 2 2 0 0 0 0 0 0 0 | 1 2 2 1 2 2 1 2 0 0 0 0 0 0 0 0 | 1 2 2 1 2 1 1 2 1 0 0 0 0 0 | 1 1 2 1 1 0
.o.. .o..    | * 2 * * | 0 1 0 0 1 2 2 0 0 0 0 | 1 2 2 0 0 0 0 0 1 2 2 1 2 0 0 0 | 1 2 2 1 2 0 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o. ..o.    | * * 2 * | 0 0 2 0 0 2 0 1 2 0 0 | 0 2 0 2 1 2 0 0 2 1 2 0 0 2 1 0 | 2 1 2 0 0 1 2 1 0 1 2 1 0 1 | 1 2 1 0 1 1
...o ...o    | * * * 4 | 0 0 0 1 0 0 1 0 1 1 1 | 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 | 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 | 1 * * * * * * * * * * | 1 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 | 0 2 0 0 2 1 0 2 1 0 0 0 0 0 | 1 0 2 1 1 0
oo.. oo..&#x | 1 1 0 0 | * 2 * * * * * * * * * | 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o. o.o.&#x | 1 0 1 0 | * * 4 * * * * * * * * | 0 1 0 1 1 1 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..o o..o&#x | 1 0 0 1 | * * * 4 * * * * * * * | 0 0 1 0 0 1 1 1 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 | * * * * 1 * * * * * * | 1 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 | 0 2 0 0 2 0 0 0 0 1 0 2 1 0 | 1 0 2 1 0 1
.oo. .oo.&#x | 0 1 1 0 | * * * * * 4 * * * * * | 0 1 0 0 0 0 0 0 1 1 1 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.o .o.o&#x | 0 1 0 1 | * * * * * * 4 * * * * | 0 0 1 0 0 0 0 0 0 0 1 1 1 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 | * * * * * * * 1 * * * | 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 | 2 0 0 0 0 1 2 0 0 1 2 0 0 1 | 1 2 0 0 1 1
..oo ..oo&#x | 0 0 1 1 | * * * * * * * * 4 * * | 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 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 | * * * * * * * * * 2 * | 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 | 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 | * * * * * * * * * * 2 | 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 | 0 0 0 0 1 0 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
-------------+---------+-----------------------+---------------------------------+-----------------------------+------------
.... xx..&#x | 2 2 0 0 | 1 2 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0
ooo. ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 0 | * 4 * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo.o oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 0 0 | * * 4 * * * * * * * * * * * * * | 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 1 0 0 0 | * * * 2 * * * * * * * * * * * * | 1 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
.... x.o.&#x | 2 0 1 0 | 1 0 2 0 0 0 0 0 0 0 0 | * * * * 2 * * * * * * * * * * * | 0 1 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0
o.oo o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 1 0 0 | * * * * * 4 * * * * * * * * * * | 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 1 0 | * * * * * * 2 * * * * * * * * * | 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 1 | * * * * * * * 2 * * * * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.ox. ....&#x | 0 1 2 0 | 0 0 0 0 0 2 0 1 0 0 0 | * * * * * * * * 2 * * * * * * * | 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.... .xo.&#x | 0 2 1 0 | 0 0 0 0 1 2 0 0 0 0 0 | * * * * * * * * * 2 * * * * * * | 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
.ooo .ooo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 1 0 0 | * * * * * * * * * * 4 * * * * * | 0 0 1 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.o.x ....&#x | 0 1 0 2 | 0 0 0 0 0 0 2 0 0 1 0 | * * * * * * * * * * * 2 * * * * | 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 1 0 2 0 0 0 1 | * * * * * * * * * * * * 2 * * * | 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..xx ....&#x | 0 0 2 2 | 0 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * * * * * 2 * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
.... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * * * 2 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
...x ...x    | 0 0 0 4 | 0 0 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
-------------+---------+-----------------------+---------------------------------+-----------------------------+------------
oox. ....&#x  1 1 2 0 | 0 1 2 0 0 2 0 1 0 0 0 | 0 2 0 1 0 0 0 0 1 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * | 1 1 0 0 0 0
.... xxo.&#x  2 2 1 0 | 1 2 2 0 1 2 0 0 0 0 0 | 1 2 0 0 1 0 0 0 0 1 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * | 1 0 1 0 0 0
oooo oooo&#x  1 1 1 1 | 0 1 1 1 0 1 1 0 1 0 0 | 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 | * * 4 * * * * * * * * * * * | 0 1 1 0 0 0
oo.x ....&#x  1 1 0 2 | 0 1 0 2 0 0 2 0 0 1 0 | 0 0 2 0 0 0 1 0 0 0 0 1 0 0 0 0 | * * * 2 * * * * * * * * * * | 0 1 0 1 0 0
.... xx.x&#x  2 2 0 2 | 1 2 0 2 1 0 2 0 0 0 1 | 1 0 2 0 0 0 0 1 0 0 0 0 1 0 0 0 | * * * * 2 * * * * * * * * * | 0 0 1 1 0 0
o.x. x.o.&#x  2 0 2 0 | 1 0 4 0 0 0 0 1 0 0 0 | 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 1 * * * * * * * * | 1 0 0 0 1 0
o.xx ....&#x  1 0 2 2 | 0 0 2 2 0 0 0 1 2 1 0 | 0 0 0 1 0 2 1 0 0 0 0 0 0 1 0 0 | * * * * * * 2 * * * * * * * | 0 1 0 0 1 0
.... x.ox&#x  2 0 1 2 | 1 0 2 2 0 0 0 0 2 0 1 | 0 0 0 0 1 2 0 1 0 0 0 0 0 0 1 0 | * * * * * * * 2 * * * * * * | 0 0 1 0 1 0
o..x x..x&#x  2 0 0 4 | 1 0 0 4 0 0 0 0 0 2 2 | 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 1 | * * * * * * * * 1 * * * * * | 0 0 0 1 1 0
.ox. .xo.&#x  0 2 2 0 | 0 0 0 0 1 4 0 1 0 0 0 | 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.oxx ....&#x  0 1 2 2 | 0 0 0 0 0 2 2 1 2 1 0 | 0 0 0 0 0 0 0 0 1 0 2 1 0 1 0 0 | * * * * * * * * * * 2 * * * | 0 1 0 0 0 1
.... .xox&#x  0 2 1 2 | 0 0 0 0 1 2 2 0 2 0 1 | 0 0 0 0 0 0 0 0 0 1 2 0 1 0 1 0 | * * * * * * * * * * * 2 * * | 0 0 1 0 0 1
.o.x .x.x&#x  0 2 0 4 | 0 0 0 0 1 0 4 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 1 | * * * * * * * * * * * * 1 * | 0 0 0 1 0 1
..xx ..ox&#x  0 0 2 4 | 0 0 0 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
-------------+---------+-----------------------+---------------------------------+-----------------------------+------------
oox. xxo.&#x  2 2 2 0 | 1 2 4 0 1 4 0 1 0 0 0 | 1 4 0 2 2 0 0 0 2 2 0 0 0 0 0 0 | 2 2 0 0 0 1 0 0 0 1 0 0 0 0 | 1 * * * * *
ooxx ....&#x  1 1 2 2 | 0 1 2 2 0 2 2 1 2 1 0 | 0 2 2 1 0 2 1 0 1 0 2 1 0 1 0 0 | 1 0 2 1 0 0 1 0 0 0 1 0 0 0 | * 2 * * * *
.... xxox&#x  2 2 1 2 | 1 2 2 2 1 2 2 0 2 0 1 | 1 2 2 0 1 2 0 1 0 1 2 0 1 0 1 0 | 0 1 2 0 1 0 0 1 0 0 0 1 0 0 | * * 2 * * *
oo.x xx.x&#x  2 2 0 4 | 1 2 0 4 1 0 4 0 0 2 2 | 1 0 4 0 0 0 2 2 0 0 0 2 2 0 0 1 | 0 0 0 2 2 0 0 0 1 0 0 0 1 0 | * * * 1 * *
o.xx x.ox&#x  2 0 2 4 | 1 0 4 4 0 0 0 1 4 2 2 | 0 0 0 2 2 4 2 2 0 0 0 0 0 2 2 1 | 0 0 0 0 0 1 2 2 1 0 0 0 0 1 | * * * * 1 *
.oxx .xox&#x  0 2 2 4 | 0 0 0 0 1 4 4 1 4 2 2 | 0 0 0 0 0 0 0 0 2 2 4 2 2 2 2 1 | 0 0 0 0 0 0 0 0 0 1 2 2 1 1 | * * * * * 1

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