Acronym coahex, co || hex
Name 1/4-lune of rectified triacontiditeron (but not octpy || octaco) ,
cuboctahedron atop hexadecachoron
Circumradius 1
Lace city
in approx. ASCII-art
       o3x4o       
                   
                   
                   
o3o4o  x3o4o  o3o4o
    x3o3o    
             
             
o3o3x   x3o3x
Coordinates
  • (1/sqrt(2), 1/sqrt(2), 0, 0, 0)   & all permutations in first 3 coords, all changes of sign
    (top co)
  • (1/sqrt(2), 0, 0, 0, 1/sqrt(2))   & all permutations in first 4 coords, all changes of sign in first 4 coords
    (bottom hex)
Confer
uniform relative:
rat  
related segmentotera:
hex || ico   octpy || octaco  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

xxo3ooo3oxx&#x   → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569
                   height(1,3) = 1/sqrt(2) = 0.707107

o..3o..3o..    | 4  * * | 3  3  3  0  0  0 0 | 3  6  3  6  3  3 0 0 0  0  0 0 | 1 3 3 1 3 3 1  6  3 0 0 0 0 0 | 1 1 3 3 1 0
.o.3.o.3.o.    | * 12 * | 0  1  0  2  2  1 0 | 0  2  2  0  0  1 1 2 1  2  2 0 | 0 1 2 1 0 0 0  2  2 1 1 2 1 0 | 1 0 1 2 1 1
..o3..o3..o    | *  * 4 | 0  0  3  0  0  3 3 | 0  0  0  3  6  3 0 0 0  3  6 3 | 0 0 0 0 1 3 3  3  6 0 1 3 3 1 | 0 1 1 3 3 1
---------------+--------+--------------------+--------------------------------+-------------------------------+------------
x.. ... ...    | 2  0 0 | 6  *  *  *  *  * * | 2  2  0  2  0  0 0 0 0  0  0 0 | 1 2 1 0 2 1 0  2  0 0 0 0 0 0 | 1 1 2 1 0 0
oo.3oo.3oo.&#x | 1  1 0 | * 12  *  *  *  * * | 0  2  2  0  0  1 0 0 0  0  0 0 | 0 1 2 1 0 0 0  2  2 0 0 0 0 0 | 1 0 1 2 1 0
o.o3o.o3o.o&#x | 1  0 1 | *  * 12  *  *  * * | 0  0  0  2  2  1 0 0 0  0  0 0 | 0 0 0 0 1 2 1  2  2 0 0 0 0 0 | 0 1 1 2 1 0
.x. ... ...    | 0  2 0 | *  *  * 12  *  * * | 0  1  0  0  0  0 1 1 0  1  0 0 | 0 1 1 0 0 0 0  1  0 1 1 1 0 0 | 1 0 1 1 0 1
... ... .x.    | 0  2 0 | *  *  *  * 12  * * | 0  0  1  0  0  0 0 1 1  0  1 0 | 0 0 1 1 0 0 0  0  1 1 0 1 1 0 | 1 0 0 1 1 1
.oo3.oo3.oo&#x | 0  1 1 | *  *  *  *  * 12 * | 0  0  0  0  0  1 0 0 0  2  2 0 | 0 0 0 0 0 0 0  2  2 0 1 2 1 0 | 0 0 1 2 1 1
... ... ..x    | 0  0 2 | *  *  *  *  *  * 6 | 0  0  0  0  2  0 0 0 0  0  2 2 | 0 0 0 0 0 1 2  0  2 0 0 1 2 1 | 0 1 0 1 2 1
---------------+--------+--------------------+--------------------------------+-------------------------------+------------
x..3o.. ...    | 3  0 0 | 3  0  0  0  0  0 0 | 4  *  *  *  *  * * * *  *  * * | 1 1 0 0 1 0 0  0  0 0 0 0 0 0 | 1 1 1 0 0 0
xx. ... ...&#x | 2  2 0 | 1  2  0  1  0  0 0 | * 12  *  *  *  * * * *  *  * * | 0 1 1 0 0 0 0  1  0 0 0 0 0 0 | 1 0 1 1 0 0
... ... ox.&#x | 1  2 0 | 0  2  0  0  1  0 0 | *  * 12  *  *  * * * *  *  * * | 0 0 1 1 0 0 0  0  1 0 0 0 0 0 | 1 0 0 1 1 0
x.o ... ...&#x | 2  0 1 | 1  0  2  0  0  0 0 | *  *  * 12  *  * * * *  *  * * | 0 0 0 0 1 1 0  1  0 0 0 0 0 0 | 0 1 1 1 0 0
... ... o.x&#x | 1  0 2 | 0  0  2  0  0  0 1 | *  *  *  * 12  * * * *  *  * * | 0 0 0 0 0 1 1  0  1 0 0 0 0 0 | 0 1 0 1 1 0
ooo3ooo3ooo&#x | 1  1 1 | 0  1  1  0  0  1 0 | *  *  *  *  * 12 * * *  *  * * | 0 0 0 0 0 0 0  2  2 0 0 0 0 0 | 0 0 1 2 1 0
.x.3.o. ...    | 0  3 0 | 0  0  0  3  0  0 0 | *  *  *  *  *  * 4 * *  *  * * | 0 1 0 0 0 0 0  0  0 1 1 0 0 0 | 1 0 1 0 0 1
.x. ... .x.    | 0  4 0 | 0  0  0  2  2  0 0 | *  *  *  *  *  * * 6 *  *  * * | 0 0 1 0 0 0 0  0  0 1 0 1 0 0 | 1 0 0 1 0 1
... .o.3.x.    | 0  3 0 | 0  0  0  0  3  0 0 | *  *  *  *  *  * * * 4  *  * * | 0 0 0 1 0 0 0  0  0 1 0 0 1 0 | 1 0 0 0 1 1
.xo ... ...&#x | 0  2 1 | 0  0  0  1  0  2 0 | *  *  *  *  *  * * * * 12  * * | 0 0 0 0 0 0 0  1  0 0 1 1 0 0 | 0 0 1 1 0 1
... ... .xx&#x | 0  2 2 | 0  0  0  0  1  2 1 | *  *  *  *  *  * * * *  * 12 * | 0 0 0 0 0 0 0  0  1 0 0 1 1 0 | 0 0 0 1 1 1
... ..o3..x    | 0  0 3 | 0  0  0  0  0  0 3 | *  *  *  *  *  * * * *  *  * 4 | 0 0 0 0 0 0 1  0  0 0 0 0 1 1 | 0 1 0 0 1 1
---------------+--------+--------------------+--------------------------------+-------------------------------+------------
x..3o..3o..     4  0 0 | 6  0  0  0  0  0 0 | 4  0  0  0  0  0 0 0 0  0  0 0 | 1 * * * * * *  *  * * * * * * | 1 1 0 0 0 0
xx.3oo. ...&#x  3  3 0 | 3  3  0  3  0  0 0 | 1  3  0  0  0  0 1 0 0  0  0 0 | * 4 * * * * *  *  * * * * * * | 1 0 1 0 0 0
xx. ... ox.&#x  2  4 0 | 1  4  0  2  2  0 0 | 0  2  2  0  0  0 0 1 0  0  0 0 | * * 6 * * * *  *  * * * * * * | 1 0 0 1 0 0
... oo.3ox.&#x  1  3 0 | 0  3  0  0  3  0 0 | 0  0  3  0  0  0 0 0 1  0  0 0 | * * * 4 * * *  *  * * * * * * | 1 0 0 0 1 0
x.o3o.o ...&#x  3  0 1 | 3  0  3  0  0  0 0 | 1  0  0  3  0  0 0 0 0  0  0 0 | * * * * 4 * *  *  * * * * * * | 0 1 1 0 0 0
x.o ... o.x&#x  2  0 2 | 1  0  4  0  0  0 1 | 0  0  0  2  2  0 0 0 0  0  0 0 | * * * * * 6 *  *  * * * * * * | 0 1 0 1 0 0
... o.o3o.x&#x  1  0 3 | 0  0  3  0  0  0 3 | 0  0  0  0  3  0 0 0 0  0  0 1 | * * * * * * 4  *  * * * * * * | 0 1 0 0 1 0
xxo ... ...&#x  2  2 1 | 1  2  2  1  0  2 0 | 0  1  0  1  0  2 0 0 0  1  0 0 | * * * * * * * 12  * * * * * * | 0 0 1 1 0 0
... ... oxx&#x  1  2 2 | 0  2  2  0  1  2 1 | 0  0  1  0  1  2 0 0 0  0  1 0 | * * * * * * *  * 12 * * * * * | 0 0 0 1 1 0
.x.3.o.3.x.     0 12 0 | 0  0  0 12 12  0 0 | 0  0  0  0  0  0 4 6 4  0  0 0 | * * * * * * *  *  * 1 * * * * | 1 0 0 0 0 1
.xo3.oo ...&#x  0  3 1 | 0  0  0  3  0  3 0 | 0  0  0  0  0  0 1 0 0  3  0 0 | * * * * * * *  *  * * 4 * * * | 0 0 1 0 0 1
.xo ... .xx&#x  0  4 2 | 0  0  0  2  2  4 1 | 0  0  0  0  0  0 0 1 0  2  2 0 | * * * * * * *  *  * * * 6 * * | 0 0 0 1 0 1
... .oo3.xx&#x  0  3 3 | 0  0  0  0  3  3 3 | 0  0  0  0  0  0 0 0 1  0  3 1 | * * * * * * *  *  * * * * 4 * | 0 0 0 0 1 1
..o3..o3..x     0  0 4 | 0  0  0  0  0  0 6 | 0  0  0  0  0  0 0 0 0  0  0 4 | * * * * * * *  *  * * * * * 1 | 0 1 0 0 0 1
---------------+--------+--------------------+--------------------------------+-------------------------------+------------
xx.3oo.3ox.&#x  4 12 0 | 6 12  0 12 12  0 0 | 4 12 12  0  0  0 4 6 4  0  0 0 | 1 4 6 4 0 0 0  0  0 1 0 0 0 0 | 1 * * * * *
x.o3o.o3o.x&#x  4  0 4 | 6  0 12  0  0  0 6 | 4  0  0 12 12  0 0 0 0  0  0 4 | 1 0 0 0 4 6 4  0  0 0 0 0 0 1 | * 1 * * * *
xxo3ooo ...&#x  3  3 1 | 3  3  3  3  0  3 0 | 1  3  0  3  0  3 1 0 0  3  0 0 | 0 1 0 0 1 0 0  3  0 0 1 0 0 0 | * * 4 * * *
xxo ... oxx&#x  2  4 2 | 1  4  4  2  2  4 1 | 0  2  2  2  2  4 0 1 0  2  2 0 | 0 0 1 0 0 1 0  2  2 0 0 1 0 0 | * * * 6 * *
... ooo3oxx&#x  1  3 3 | 0  3  3  0  3  3 3 | 0  0  3  0  3  3 0 0 1  0  3 1 | 0 0 0 1 0 0 1  0  3 0 0 0 1 0 | * * * * 4 *
.xo3.oo3.xx&#x  0 12 4 | 0  0  0 12 12 12 6 | 0  0  0  0  0  0 4 6 4 12 12 4 | 0 0 0 0 0 0 0  0  0 1 4 6 4 1 | * * * * * 1

x.o3o.o3o.x&#x || .x.3.o.3.x.   → height = 1/sqrt(2) = 0.707107
(hex || co)

o..3o..3o..    & | 8  * |  3  3  3  0 | 3  6  3  9  3 0 0 | 1 3  3 1 4 3  9 0 | 1 1 4 3
.o.3.o.3.o.      | * 12 |  0  2  0  4 | 0  4  4  0  1 2 2 | 0 2  4 2 0 0  4 1 | 2 0 2 2
-----------------+------+-------------+-------------------+-------------------+--------
x.. ... ...    & | 2  0 | 12  *  *  * | 2  2  0  2  0 0 0 | 1 2  1 0 2 1  2 0 | 1 1 2 1
oo.3oo.3oo.&#x & | 1  1 |  * 24  *  * | 0  2  2  0  1 0 0 | 0 1  2 1 0 0  4 0 | 1 0 2 2
o.o3o.o3o.o&#x   | 2  0 |  *  * 12  * | 0  0  0  4  1 0 0 | 0 0  0 0 2 2  4 0 | 0 1 2 2
.x. ... ...    & | 0  2 |  *  *  * 24 | 0  1  1  0  0 1 1 | 0 1  2 1 0 0  1 1 | 2 0 1 1
-----------------+------+-------------+-------------------+-------------------+--------
x..3o.. ...    & | 3  0 |  3  0  0  0 | 8  *  *  *  * * * | 1 1  0 0 1 0  0 0 | 1 1 1 0
xx. ... ...&#x & | 2  2 |  1  2  0  1 | * 24  *  *  * * * | 0 1  1 0 0 0  1 0 | 1 0 1 1
... ... ox.&#x & | 1  2 |  0  2  0  1 | *  * 24  *  * * * | 0 0  1 1 0 0  1 0 | 1 0 1 1
x.o ... ...&#x & | 3  0 |  1  0  2  0 | *  *  * 24  * * * | 0 0  0 0 1 1  1 0 | 0 1 1 1
ooo3ooo3ooo&#x   | 2  1 |  0  2  1  0 | *  *  *  * 12 * * | 0 0  0 0 0 0  4 0 | 0 0 2 2
.x.3.o. ...    & | 0  3 |  0  0  0  3 | *  *  *  *  * 8 * | 0 1  0 1 0 0  0 1 | 2 0 1 0
.x. ... .x.      | 0  4 |  0  0  0  4 | *  *  *  *  * * 6 | 0 0  2 0 0 0  0 1 | 2 0 0 1
-----------------+------+-------------+-------------------+-------------------+--------
x..3o..3o..    &  4  0 |  6  0  0  0 | 4  0  0  0  0 0 0 | 2 *  * * * *  * * | 1 1 0 0
xx.3oo. ...&#x &  3  3 |  3  3  0  3 | 1  3  0  0  0 1 0 | * 8  * * * *  * * | 1 0 1 0
xx. ... ox.&#x &  2  4 |  1  4  0  4 | 0  2  2  0  0 0 1 | * * 12 * * *  * * | 1 0 0 1
... oo.3ox.&#x &  1  3 |  0  3  0  3 | 0  0  3  0  0 1 0 | * *  * 8 * *  * * | 1 0 1 0
x.o3o.o ...&#x &  4  0 |  3  0  3  0 | 1  0  0  3  0 0 0 | * *  * * 8 *  * * | 0 1 1 0
x.o ... o.x&#x    4  0 |  2  0  4  0 | 0  0  0  4  0 0 0 | * *  * * * 6  * * | 0 1 0 1
xxo ... ...&#x &  3  2 |  1  4  2  1 | 0  1  1  1  2 0 0 | * *  * * * * 24 * | 0 0 1 1
.x.3.o.3.x.       0 12 |  0  0  0 24 | 0  0  0  0  0 8 6 | * *  * * * *  * 1 | 2 0 0 0
-----------------+------+-------------+-------------------+-------------------+--------
xx.3oo.3ox.&#x &  4 12 |  6 12  0 24 | 4 12 12  0  0 8 6 | 1 4  6 4 0 0  0 1 | 2 * * *
x.o3o.o3o.x&#x    8  0 | 12  0 12  0 | 8  0  0 24  0 0 0 | 2 0  0 0 8 6  0 0 | * 1 * *
xxo3ooo ...&#x &  4  3 |  3  6  3  3 | 1  3  3  3  3 1 0 | 0 1  0 1 1 0  3 0 | * * 8 *
xxo ... oxx&#x    4  4 |  2  8  4  4 | 0  4  4  4  4 0 1 | 0 0  2 0 0 1  4 0 | * * * 6

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