Acronym hexaico, hex || ico
Name hexadecachoron-first rotunda of rectified triacontiditeron,
hexadecachoron atop icositetrachoron
Circumradius 1
Lace city
in approx. ASCII-art
o3o4o  x3o4o  o3o4o
                   
                   
                   
x3o4o  o3x4o  x3o4o
    x3o3o   o3x3o
                 
                 
o3o3x   x3o3x    
                 
                 
    o3x3o        
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign, but last coord non-negative
Confer
uniform relative:
rat  
related segmentotera:
co || hex  
general polytopal classes:
segmentotera   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

xo3ox3oo4oo&#x   → height = 1/sqrt(2) = 0.707107
(hex || ico)

o.3o.3o.4o.    | 8  *   6  6  0 | 12  6 12  0  0 |  8 12  8  0 0 | 1  8 1 0
.o3.o3.o4.o    | * 24   0  2  8 |  0  1  8  4  8 |  0  4  8  4 2 | 0  4 2 1
---------------+------+----------+----------------+---------------+---------
x. .. .. ..    | 2  0 | 24  *  *   4  1  0  0  0 |  4  4  0  0 0 | 1  4 0 0
oo3oo3oo4oo&#x | 1  1 |  * 48  * |  0  1  4  0  0 |  0  4  4  0 0 | 0  4 1 0
.. .x .. ..    | 0  2 |  *  * 96 |  0  0  1  1  2 |  0  1  2  2 1 | 0  2 1 1
---------------+------+----------+----------------+---------------+---------
x.3o. .. ..    | 3  0 |  3  0  0 | 32  *  *  *  * |  2  1  0  0 0 | 1  2 0 0
xo .. .. ..&#x | 2  1 |  1  2  0 |  * 24  *  *  * |  0  4  0  0 0 | 0  4 0 0
.. ox .. ..&#x | 1  2 |  0  2  1 |  *  * 96  *  * |  0  1  2  0 0 | 0  2 1 0
.o3.x .. ..    | 0  3 |  0  0  3 |  *  *  * 32  * |  0  1  0  2 0 | 0  2 0 1
.. .x3.o ..    | 0  3 |  0  0  3 |  *  *  *  * 64 |  0  0  1  1 8 | 0  1 1 1
---------------+------+----------+----------------+---------------+---------
x.3o.3o. ..     4  0 |  6  0  0 |  4  0  0  0  0 | 16  *  *  * * | 1  1 0 0
xo3ox .. ..&#x  3  3 |  3  6  3 |  1  3  3  1  0 |  * 32  *  * * | 0  2 0 0
.. ox3oo ..&#x  1  3 |  0  3  3 |  0  0  3  0  1 |  *  * 64  * * | 0  1 1 0
.o3.x3.o ..     0  6 |  0  0 12 |  0  0  0  4  4 |  *  *  * 16 * | 0  1 0 1
.. .x3.o4.o     0  6 |  0  0 12 |  0  0  0  0  8 |  *  *  *  * 8 | 0  0 1 1
---------------+------+----------+----------------+---------------+---------
x.3o.3o.4o.     8  0 | 24  0  0 | 32  0  0  0  0 | 16  0  0  0 0 | 1  * * *
xo3ox3oo ..&#x  4  6 |  6 12 12 |  4  6 12  4  4 |  1  4  4  1 0 | * 16 * *
.. ox3oo4oo&#x  1  6 |  0  6 12 |  0  0 12  0  8 |  0  0  8  0 1 | *  * 8 *
.o3.x3.o4.o     0 24 |  0  0 96 |  0  0  0 32 64 |  0  0  0 16 8 | *  * * 1

oo3ox3oo *b3xo&#x   → height = 1/sqrt(2) = 0.707107
(hex || ico)

o.3o.3o. *b3o.    | 8  *   6  6  0 | 12 12  6  0  0  0 | 4 4  4  4 12 0 0 0 | 1 4 4 1 0
.o3.o3.o *b3.o    | * 24   0  2  8 |  0  8  1  4  4  4 | 0 0  4  4  4 2 2 2 | 0 2 2 2 1
------------------+------+----------+-------------------+--------------------+----------
.. .. ..    x.    | 2  0 | 24  *  *   4  0  1  0  0  0 | 2 2  0  0  4 0 0 0 | 1 2 2 0 0
oo3oo3oo *b3oo&#x | 1  1 |  * 48  * |  0  4  1  0  0  0 | 0 0  2  2  4 0 0 0 | 0 2 2 1 0
.. .x ..    ..    | 0  2 |  *  * 96 |  0  1  0  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
------------------+------+----------+-------------------+--------------------+----------
.. o. .. *b3x.    | 3  0 |  3  0  0 | 32  *  *  *  *  * | 1 1  0  0  1 0 0 0 | 1 1 1 0 0
.. ox ..    ..&#x | 1  2 |  0  2  1 |  * 96  *  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.. .. ..    xo&#x | 2  1 |  1  2  0 |  *  * 24  *  *  * | 0 0  0  0  4 0 0 0 | 0 2 2 0 0
.o3.x ..    ..    | 0  3 |  0  0  3 |  *  *  * 32  *  * | 0 0  1  0  0 1 1 0 | 0 1 0 1 1
.. .x3.o    ..    | 0  3 |  0  0  3 |  *  *  *  * 32  * | 0 0  0  1  0 1 0 1 | 0 0 1 1 1
.. .x .. *b3.o    | 0  3 |  0  0  3 |  *  *  *  *  * 32 | 0 0  0  0  1 0 1 1 | 0 1 1 0 1
------------------+------+----------+-------------------+--------------------+----------
o.3o. .. *b3x.     4  0 |  6  0  0 |  4  0  0  0  0  0 | 8 *  *  *  * * * * | 1 1 0 0 0
.. o.3o. *b3x.     4  0 |  6  0  0 |  4  0  0  0  0  0 | * 8  *  *  * * * * | 1 0 1 0 0
oo3ox ..    ..&#x  1  3 |  0  3  3 |  0  3  0  1  0  0 | * * 32  *  * * * * | 0 1 0 1 0
.. ox3oo    ..&#x  1  3 |  0  3  3 |  0  3  0  0  1  0 | * *  * 32  * * * * | 0 0 1 1 0
.. ox .. *b3xo&#x  3  3 |  3  6  3 |  1  3  3  0  0  1 | * *  *  * 32 * * * | 0 1 1 0 0
.o3.x3.o    ..     0  6 |  0  0 12 |  0  0  0  4  4  0 | * *  *  *  * 8 * * | 0 0 0 1 1
.o3.x .. *b3.o     0  6 |  0  0 12 |  0  0  0  4  0  4 | * *  *  *  * * 8 * | 0 1 0 0 1
.. .x3.o *b3.o     0  6 |  0  0 12 |  0  0  0  0  4  4 | * *  *  *  * * * 8 | 0 0 1 0 1
------------------+------+----------+-------------------+--------------------+----------
o.3o.3o. *b3x.     8  0 | 24  0  0 | 32  0  0  0  0  0 | 8 8  0  0  0 0 0 0 | 1 * * * *
oo3ox .. *b3xo&#x  4  6 |  6 12 12 |  4 12  6  4  0  4 | 1 0  4  0  4 0 1 0 | * 8 * * *
.. ox3oo *b3xo&#x  4  6 |  6 12 12 |  4 12  6  0  4  4 | 0 1  0  4  4 0 0 1 | * * 8 * *
oo3ox3oo    ..&#x  1  6 |  0  6 12 |  0 12  0  4  4  0 | 0 0  4  4  0 1 0 0 | * * * 8 *
.o3.x3.o *b3.o     0 24 |  0  0 96 |  0  0  0 32 32 32 | 0 0  0  0  0 8 8 8 | * * * * 1

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