Acronym coaescu, co || escu, K-4.62
Name cuboctahedron atop elongated square cupola
Segmentochoron display
Circumradius (1+sqrt(8))/sqrt(7) = 1.447009
Lace city
in approx. ASCII-art 
            +---------- squap
          /         +-- squacu
        /          /

     A     B     C 
    x4o   o4q   x4o	-- co
                   
o4x   x4x     x4x  	-- escu
 D     E       F
Face vector 32, 100, 92, 24
Confer
related segmentochora:
coasirco   coaop   antitetrawedge  
general polytopal classes:
segmentochora  

Incidence matrix according to Dynkin symbol

xox4oqo&#xt || oxx4xxx&#xt   → height = sqrt[2 sqrt(2)-1]/2 = 0.676097
(co || escu)

o..4o..       ... ...     | 4 * * * * * | 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 2 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 1 1 0 0 0 0  A
.o.4.o.       ... ...     | * 4 * * * * | 0 2 0 0 2 2 2 0 0 0 0 0 0 0 0 0 | 0 1 2 1 0 2 0 0 0 0 2 1 2 1 0 0 0 0 0 0 0 0 | 1 1 0 0 2 1 1 0 0  B
..o4..o       ... ...     | * * 4 * * * | 0 0 0 0 2 0 0 2 2 0 0 0 0 0 0 0 | 0 0 1 2 1 0 0 0 0 0 2 0 0 0 2 1 0 0 0 0 0 0 | 1 0 0 0 1 2 0 1 0  C
... ...       o..4o..     | * * * 4 * * | 0 0 2 0 0 0 0 0 0 2 2 0 0 0 0 0 | 0 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 1 1 2 0 0 0 | 0 1 1 2 0 0 0 0 1  D
... ...       .o.4.o.     | * * * * 8 * | 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 | 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 | 0 1 0 1 1 0 1 0 1  E
... ...       ..o4..o     | * * * * * 8 | 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 | 0 0 0 0 1 1 1 1 1  F
--------------------------+-------------+---------------------------------+---------------------------------------------+------------------
x.. ...       ... ...     | 2 0 0 0 0 0 | 4 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0
oo.4oo.&#x    ... ...     | 1 1 0 0 0 0 | * 8 * * * * * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 0 1 0 0 0 0
o..4o..     || o..4o..     | 1 0 0 1 0 0 | * * 8 * * * * * * * * * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 0
o..4o..     || .o.4.o.     | 1 0 0 0 1 0 | * * * 8 * * * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 1 0 0 0 0
.oo4.oo&#x    ... ...     | 0 1 1 0 0 0 | * * * * 8 * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 1 1 0 0 0
.o.4.o.     || .o.4.o.     | 0 1 0 0 1 0 | * * * * * 8 * * * * * * * * * * | 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 | 0 1 0 0 1 0 1 0 0
.o.4.o.     || ..o4..o     | 0 1 0 0 0 1 | * * * * * * 8 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 0 0
..x ...       ... ...     | 0 0 2 0 0 0 | * * * * * * * 4 * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 1 0 0 0 0 1 0 1 0
..o4..o     || ..o4..o     | 0 0 1 0 0 1 | * * * * * * * * 8 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 | 0 0 0 0 1 1 0 1 0
... ...       ... x..     | 0 0 0 2 0 0 | * * * * * * * * * 4 * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 | 0 0 1 1 0 0 0 0 1
... ...       oo.4oo.&#x  | 0 0 0 1 1 0 | * * * * * * * * * * 8 * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 0 1 0 1 0 0 0 0 1
... ...       .x. ...     | 0 0 0 0 2 0 | * * * * * * * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 | 0 1 0 0 0 0 1 0 1
... ...       ... .x.     | 0 0 0 0 2 0 | * * * * * * * * * * * * 4 * * * | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 | 0 0 0 1 1 0 0 0 1
... ...       .oo4.oo&#x  | 0 0 0 0 1 1 | * * * * * * * * * * * * * 8 * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 0 0 1 0 1 0 1
... ...       ..x ...     | 0 0 0 0 0 2 | * * * * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 | 0 0 0 0 0 1 1 1 1
... ...       ... ..x     | 0 0 0 0 0 2 | * * * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 | 0 0 0 0 1 0 0 1 1
--------------------------+-------------+---------------------------------+---------------------------------------------+------------------
x..4o..       ... ...     | 4 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0
xo. ...&#x    ... ...     | 2 1 0 0 0 0 | 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0
... oqo&#xt   ... ...     | 1 2 1 0 0 0 | 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * * * * * * * * * | 1 0 0 0 1 0 0 0 0
.ox ...&#x    ... ...     | 0 1 2 0 0 0 | 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 | * * * 4 * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 1 0 0 0
..x4..o       ... ...     | 0 0 4 0 0 0 | 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 | * * * * 1 * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 0 1 0
oo.4oo.&#x  || .o.4.o.     | 1 1 0 0 1 0 | 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 | * * * * * 8 * * * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0
x.. ...     || o..4o..     | 2 0 0 1 0 0 | 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 4 * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 0
o..4o..     || ... x..     | 1 0 0 2 0 0 | 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 | * * * * * * * 4 * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0
o..4o..     || oo.4oo.&#x  | 1 0 0 1 1 0 | 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 | * * * * * * * * 8 * * * * * * * * * * * * * | 0 1 0 1 0 0 0 0 0
o..4o..     || ... .x.     | 1 0 0 0 2 0 | 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 | * * * * * * * * * 4 * * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0
.oo4.oo&#x  || ..o4..o     | 0 1 1 0 0 1 | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 | * * * * * * * * * * 8 * * * * * * * * * * * | 0 0 0 0 1 1 0 0 0
.o.4.o.     || .x. ...     | 0 1 0 0 2 0 | 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 | * * * * * * * * * * * 4 * * * * * * * * * * | 0 1 0 0 0 0 1 0 0
.o.4.o.     || .oo4.oo&#x  | 0 1 0 0 1 1 | 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 | * * * * * * * * * * * * 8 * * * * * * * * * | 0 0 0 0 1 0 1 0 0
.o.4.o.     || ..x ...     | 0 1 0 0 0 2 | 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 | * * * * * * * * * * * * * 4 * * * * * * * * | 0 0 0 0 0 1 1 0 0
..x ...     || ..x ...     | 0 0 2 0 0 2 | 0 0 0 0 0 0 0 1 2 0 0 0 0 0 1 0 | * * * * * * * * * * * * * * 4 * * * * * * * | 0 0 0 0 0 1 0 1 0
..o4..o     || ... ..x     | 0 0 1 0 0 2 | 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 | * * * * * * * * * * * * * * * 4 * * * * * * | 0 0 0 0 1 0 0 1 0
... ...       o..4x..     | 0 0 0 4 0 0 | 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 | * * * * * * * * * * * * * * * * 1 * * * * * | 0 0 1 0 0 0 0 0 1
... ...       ox. ...&#x  | 0 0 0 1 2 0 | 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 | * * * * * * * * * * * * * * * * * 4 * * * * | 0 1 0 0 0 0 0 0 1
... ...       ... xx.&#x  | 0 0 0 2 2 0 | 0 0 0 0 0 0 0 0 0 1 2 0 1 0 0 0 | * * * * * * * * * * * * * * * * * * 4 * * * | 0 0 0 1 0 0 0 0 1
... ...       .xx ...&#x  | 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 | * * * * * * * * * * * * * * * * * * * 4 * * | 0 0 0 0 0 0 1 0 1
... ...       ... .xx&#x  | 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * * * * * * * * * * 4 * | 0 0 0 0 1 0 0 0 1
... ...       ..x4..x     | 0 0 0 0 0 8 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 1 1
--------------------------+-------------+---------------------------------+---------------------------------------------+------------------
xox4oqo&#xt   ... ...     ♦ 4 4 4 0 0 0 | 4 8 0 0 8 0 0 4 0 0 0 0 0 0 0 0 | 1 4 4 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * *
xo. ...&#x  || ox. ...&#x  ♦ 2 1 0 1 2 0 | 1 2 2 2 0 2 0 0 0 0 2 1 0 0 0 0 | 0 1 0 0 0 2 1 0 2 0 0 1 0 0 0 0 0 1 0 0 0 0 | * 4 * * * * * * *
x..4o..     || o..4x..     ♦ 4 0 0 4 0 0 | 4 0 8 0 0 0 0 0 0 4 0 0 0 0 0 0 | 1 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | * * 1 * * * * * *
o..4o..     || ... xx.&#x  ♦ 1 0 0 2 2 0 | 0 0 2 2 0 0 0 0 0 1 2 0 1 0 0 0 | 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 0 0 0 | * * * 4 * * * * *
... oqo&#xt || ... .xx&#x  ♦ 1 2 1 0 2 2 | 0 2 0 2 2 2 2 0 2 0 0 0 1 2 0 1 | 0 0 1 0 0 2 0 0 0 1 2 0 2 0 0 1 0 0 0 0 1 0 | * * * * 4 * * * *
.ox ...&#x  || ..x ...     ♦ 0 1 2 0 0 2 | 0 0 0 0 2 0 2 1 2 0 0 0 0 0 1 0 | 0 0 0 1 0 0 0 0 0 0 2 0 0 1 1 0 0 0 0 0 0 0 | * * * * * 4 * * *
.o.4.o.     || .xx ...&#x  ♦ 0 1 0 0 2 2 | 0 0 0 0 0 2 2 0 0 0 0 1 0 2 1 0 | 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 1 0 0 | * * * * * * 4 * *
..x4..o     || ..x4..x     ♦ 0 0 4 0 0 8 | 0 0 0 0 0 0 0 4 8 0 0 0 0 0 4 4 | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 1 | * * * * * * * 1 *
... ...       oxx4xxx&#xt ♦ 0 0 0 4 8 8 | 0 0 0 0 0 0 0 0 0 4 8 4 4 8 4 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 4 4 4 1 | * * * * * * * * 1

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