Acronym bidoctaco, {4} || co, K-4.28
Name square atop cuboctahedron,
bidiminished octaco,
square first rotunda of cytau tes
Segmentochoron display
Circumradius 1
Lace city
in approx. ASCII-art
     x4o     
             
x4o  o4q  x4o
Dihedral angles
Confer
uniform relative:
ico  
related segmentochora:
octaco  
related CRFs:
oct || co || co || oct   cytau tes  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

x4o || xox4oqo&#xt   → height = 1/sqrt(2) = 0.707107
({4} || co)

o4o   ... ...       | 4 * * | 2 2 2 0  0 | 1 4  4 2 0 0 0 | 2 4 1 0
. .   o..4o..     & | * 8 * | 0 1 0 2  2 | 0 2  2 0 1 2 1 | 1 2 1 1
. .   .o.4.o.       | * * 4 | 0 0 2 0  4 | 0 0  4 1 0 2 2 | 0 2 2 1
--------------------+-------+------------+----------------+--------
x .   ... ...       | 2 0 0 | 4 * * *  * | 1 2  0 1 0 0 0 | 2 2 0 0
o4o || o..4o..     & | 1 1 0 | * 8 * *  * | 0 2  2 0 0 0 0 | 1 2 1 0
o4o || .o.4.o.       | 1 0 1 | * * 8 *  * | 0 0  2 1 0 0 0 | 0 2 1 0
. .   x.. ...     & | 0 2 0 | * * * 8  * | 0 1  0 0 1 1 0 | 1 1 0 1
. .   oo.4oo.&#x  & | 0 1 1 | * * * * 16 | 0 0  1 0 0 1 1 | 0 1 1 1
--------------------+-------+------------+----------------+--------
x4o   ... ...       | 4 0 0 | 4 0 0 0  0 | 1 *  * * * * * | 2 0 0 0
x . || x.. ...     & | 2 2 0 | 1 2 0 1  0 | * 8  * * * * * | 1 1 0 0
o4o || oo.4oo.&#x  & | 1 1 1 | 0 1 1 0  1 | * * 16 * * * * | 0 1 1 0
x . || .o.4.o.       | 2 0 1 | 1 0 2 0  0 | * *  * 4 * * * | 0 2 0 0
. .   x..4o..     & | 0 4 0 | 0 0 0 4  0 | * *  * * 2 * * | 1 0 0 1
. .   xo. ...&#x  & | 0 2 1 | 0 0 0 1  2 | * *  * * * 8 * | 0 1 0 1
. .   ... oqo&#xt   | 0 2 2 | 0 0 0 0  4 | * *  * * * * 4 | 0 0 1 1
--------------------+-------+------------+----------------+--------
x4o || x..4o..     &  4 4 0 | 4 4 0 4  0 | 1 4  0 0 1 0 0 | 2 * * *
x . || xo. ...&#x  &  2 2 1 | 1 2 2 1  2 | 0 1  2 1 0 1 0 | * 8 * *
o4o || ... oqo&#xt    1 2 2 | 0 2 2 0  4 | 0 0  4 0 0 0 1 | * * 4 *
. .   xox4oqo&#xt    0 8 4 | 0 0 0 8 16 | 0 0  0 0 2 8 4 | * * * 1

xxxo4oooq&#xr   → height(1,2) = height(2,3) = 1
                  height(1,4) = height(2,4) = height(3,4) = height(2,134) = 1/sqrt(2) = 0.707107

o...4o...     | 4 * * * | 2 1 2 0 0 0 0 0 | 1 2 2 2 1 0 0 0 0 0 0 | 1 2 1 1 0 0
.o..4.o..     | * 4 * * | 0 1 0 2 1 2 0 0 | 0 2 0 2 0 1 2 2 2 0 0 | 1 2 0 1 1 2
..o.4..o.     | * * 4 * | 0 0 0 0 1 0 2 2 | 0 0 0 0 1 0 2 0 2 1 2 | 0 0 1 1 1 2
...o4...o     | * * * 4 | 0 0 2 0 0 2 0 2 | 0 0 1 2 2 0 0 1 2 0 1 | 0 1 1 2 0 1
--------------+---------+-----------------+-----------------------+------------
x... ....     | 2 0 0 0 | 4 * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
oo..4oo..&#x  | 1 1 0 0 | * 4 * * * * * * | 0 2 0 2 0 0 0 0 0 0 0 | 1 2 0 1 0 0
o..o4o..o&#x  | 1 0 0 1 | * * 8 * * * * * | 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
.x.. ....     | 0 2 0 0 | * * * 4 * * * * | 0 1 0 0 0 1 1 1 0 0 0 | 1 1 0 0 1 1
.oo.4.oo.&#x  | 0 1 1 0 | * * * * 4 * * * | 0 0 0 0 0 0 2 0 2 0 0 | 0 0 0 1 1 2
.o.o4.o.o&#x  | 0 1 0 1 | * * * * * 8 * * | 0 0 0 1 0 0 0 1 1 0 0 | 0 1 0 1 0 1
..x. ....     | 0 0 2 0 | * * * * * * 4 * | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 0 1 1
..oo4..oo&#x  | 0 0 1 1 | * * * * * * * 8 | 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 1 0 1
--------------+---------+-----------------+-----------------------+------------
x...4o...     | 4 0 0 0 | 4 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 0 1 0 0 0
xx.. ....&#x  | 2 2 0 0 | 1 2 0 1 0 0 0 0 | * 4 * * * * * * * * * | 1 1 0 0 0 0
x..o ....&#x  | 2 0 0 1 | 1 0 2 0 0 0 0 0 | * * 4 * * * * * * * * | 0 1 1 0 0 0
oo.o4oo.o&#x  | 1 1 0 1 | 0 1 1 0 0 1 0 0 | * * * 8 * * * * * * * | 0 1 0 1 0 0
.... o.oq&#x  | 1 0 1 2 | 0 0 2 0 0 0 0 2 | * * * * 4 * * * * * * | 0 0 1 1 0 0
.x..4.o..     | 0 4 0 0 | 0 0 0 4 0 0 0 0 | * * * * * 1 * * * * * | 1 0 0 0 1 0
.xx. ....&#x  | 0 2 2 0 | 0 0 0 1 2 0 1 0 | * * * * * * 4 * * * * | 0 0 0 0 1 1
.x.o ....&#x  | 0 2 0 1 | 0 0 0 1 0 2 0 0 | * * * * * * * 4 * * * | 0 1 0 0 0 1
.ooo4.ooo&#x  | 0 1 1 1 | 0 0 0 0 1 1 0 1 | * * * * * * * * 8 * * | 0 0 0 1 0 1
..x.4..o.     | 0 0 4 0 | 0 0 0 0 0 0 4 0 | * * * * * * * * * 1 * | 0 0 1 0 1 0
..xo ....&#x  | 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * * * * * * 4 | 0 0 1 0 0 1
--------------+---------+-----------------+-----------------------+------------
xx..4oo..&#x   4 4 0 0 | 4 4 0 4 0 0 0 0 | 1 4 0 0 0 1 0 0 0 0 0 | 1 * * * * *
xx.o ....&#x   2 2 0 1 | 1 2 2 1 0 2 0 0 | 0 1 1 2 0 0 0 1 0 0 0 | * 4 * * * *
x.xo4o.oq&#xr  4 0 4 4 | 4 0 8 0 0 0 4 8 | 1 0 4 0 4 0 0 0 0 1 4 | * * 1 * * *
.... oooq&#xr  1 1 1 2 | 0 1 2 0 1 2 0 2 | 0 0 0 2 1 0 0 0 2 0 0 | * * * 4 * *
.xx.4.oo.&#x   0 4 4 0 | 0 0 0 4 4 0 4 0 | 0 0 0 0 0 1 4 0 0 1 0 | * * * * 1 *
.xxo ....&#x   0 2 2 1 | 0 0 0 1 2 2 1 2 | 0 0 0 0 0 0 1 1 2 0 1 | * * * * * 4
or
o...4o...     & | 8 * * | 2 1  2 0 0 | 1 2 2  2 1 0 0 | 1 2 1 1
.o..4.o..       | * 4 * | 0 2  0 2 2 | 0 4 0  4 0 1 2 | 2 4 0 1
...o4...o       | * * 4 | 0 0  4 0 2 | 0 0 2  4 2 0 1 | 0 2 1 2
----------------+-------+------------+----------------+--------
x... ....     & | 2 0 0 | 8 *  * * * | 1 1 1  0 0 0 0 | 1 1 1 0
oo..4oo..&#x  & | 1 1 0 | * 8  * * * | 0 2 0  2 0 0 0 | 1 2 0 1
o..o4o..o&#x  & | 1 0 1 | * * 16 * * | 0 0 1  1 1 0 0 | 0 1 1 1
.x.. ....       | 0 2 0 | * *  * 4 * | 0 2 0  0 0 1 1 | 2 2 0 0
.o.o4.o.o&#x    | 0 1 1 | * *  * * 8 | 0 0 0  2 0 0 1 | 0 2 0 1
----------------+-------+------------+----------------+--------
x...4o...     & | 4 0 0 | 4 0  0 0 0 | 2 * *  * * * * | 1 0 1 0
xx.. ....&#x  & | 2 2 0 | 1 2  0 1 0 | * 8 *  * * * * | 1 1 0 0
x..o ....&#x  & | 2 0 1 | 1 0  2 0 0 | * * 8  * * * * | 0 1 1 0
oo.o4oo.o&#x  & | 1 1 1 | 0 1  1 0 1 | * * * 16 * * * | 0 1 0 1
.... o.oq&#x    | 2 0 2 | 0 0  4 0 0 | * * *  * 4 * * | 0 0 1 1
.x..4.o..       | 0 4 0 | 0 0  0 4 0 | * * *  * * 1 * | 2 0 0 0
.x.o ....&#x    | 0 2 1 | 0 0  0 1 2 | * * *  * * * 4 | 0 2 0 0
----------------+-------+------------+----------------+--------
xx..4oo..&#x  &  4 4 0 | 4 4  0 4 0 | 1 4 0  0 0 1 0 | 2 * * *
xx.o ....&#x  &  2 2 1 | 1 2  2 1 2 | 0 1 1  2 0 0 1 | * 8 * *
x.xo4o.oq&#xr    8 0 4 | 8 0 16 0 0 | 2 0 8  0 4 0 0 | * * 1 *
.... oooq&#xr    2 1 2 | 0 2  4 0 2 | 0 0 0  4 1 0 0 | * * * 4

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