Acronym icarit, ico || rit
Name icositetrachoron atop rectified tesseract,
ico-first half of nit
Circumradius sqrt(3/2) = 1.224745
Lace city
in approx. ASCII-art
x3o4o   o3x4o   x3o4o
                     
                     
                     
                     
o3x4o   o3o4u   o3x4o
   o3x3o x3o3x o3x3o   
                       
                       
                       
x3o3o x3x3o o3x3x o3o3x
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign, but last coord non-negative
Confer
uniform relative:
nit  
related segmentotera:
ica tutcup   coarit   octco tuttric  
general polytopal classes:
segmentotera   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

oo3xo3ox4oo&#x   → height = 1/sqrt(2) = 0.707107
(ico || rit)

o.3o.3o.4o.    | 24  *   8  4  0 |  4  8  8  4  0  0 |  4 2  4  8  1  0 0 | 1  4 2 0
.o3.o3.o4.o    |  * 32 |  0  3  6 |  0  0  3  6  6  3 |  0 0  1  6  3  2 3 | 0  2 3 1
---------------+-------+----------+-------------------+--------------------+---------
.. x. .. ..    |  2  0 | 96  *  * |  1  2  1  0  0  0 |  2 1  1  2  0  0 0 | 1  2 1 0
oo3oo3oo4oo&#x |  1  1 |  * 96  * |  0  0  2  2  0  0 |  0 0  1  4  1  0 0 | 0  2 2 0
.. .. .x ..    |  0  2 |  *  * 96 |  0  0  0  1  2  1 |  0 0  0  2  1  1 2 | 0  1 2 1
---------------+-------+----------+-------------------+--------------------+---------
o.3x. .. ..    |  3  0 |  3  0  0 | 32  *  *  *  *  * |  2 0  1  0  0  0 0 | 1  2 0 0
.. x.3o. ..    |  3  0 |  3  0  0 |  * 64  *  *  *  * |  1 1  0  1  0  0 0 | 1  1 1 0
.. xo .. ..&#x |  2  1 |  1  2  0 |  *  * 96  *  *  * |  0 0  1  2  0  0 0 | 0  2 1 0
.. .. ox ..&#x |  1  2 |  0  2  1 |  *  *  * 96  *  * |  0 0  0  2  1  0 0 | 0  1 2 0
.. .o3.x ..    |  0  3 |  0  0  3 |  *  *  *  * 64  * |  0 0  0  1  0  1 1 | 0  1 1 1
.. .. .x4.o    |  0  4 |  0  0  4 |  *  *  *  *  * 24 |  0 0  0  0  1  0 2 | 0  0 2 1
---------------+-------+----------+-------------------+--------------------+---------
o.3x.3o. ..      6  0 | 12  0  0 |  4  4  0  0  0  0 | 16 *  *  *  *  * * | 1  1 0 0
.. x.3o.4o.      6  0 | 12  0  0 |  0  8  0  0  0  0 |  * 8  *  *  *  * * | 1  0 1 0
oo3xo .. ..&#x   3  1 |  3  3  0 |  1  0  3  0  0  0 |  * * 32  *  *  * * | 0  2 0 0
.. xo3ox ..&#x   3  3 |  3  6  3 |  0  1  3  3  1  0 |  * *  * 64  *  * * | 0  1 1 0
.. .. ox4oo&#x   1  4 |  0  4  4 |  0  0  0  4  0  1 |  * *  *  * 24  * * | 0  0 2 0
.o3.o3.x ..      0  4 |  0  0  6 |  0  0  0  0  4  0 |  * *  *  *  * 16 * | 0  1 0 1
.. .o3.x4.o      0 12 |  0  0 24 |  0  0  0  0  8  6 |  * *  *  *  *  * 8 | 0  0 1 1
---------------+-------+----------+-------------------+--------------------+---------
o.3x.3o.4o.     24  0 | 96  0  0 | 32 64  0  0  0  0 | 16 8  0  0  0  0 0 | 1  * * *
oo3xo3ox ..&#x   6  4 | 12 12  6 |  4  4 12  6  4  0 |  1 0  4  4  0  1 0 | * 16 * *
.. xo3ox4oo&#x   6 12 | 12 24 24 |  0  8 12 24  8  6 |  0 1  0  8  6  0 1 | *  * 8 *
.o3.o3.x4.o      0 32 |  0  0 96 |  0  0  0  0 64 24 |  0 0  0  0  0 16 8 | *  * * 1

ox3xo3ox *b3oo&#x   → height = 1/sqrt(2) = 0.707107
(ico || rit)

o.3o.3o. *b3o.    | 24  *   8  4  0  0 |  4  4  4  2  8  2  0  0  0 | 2 2 2  4  1  4  4 0 0 0 | 1 2 2 2 0
.o3.o3.o *b3.o    |  * 32 |  0  3  3  3 |  0  0  0  3  3  3  3  3  3 | 0 0 0  3  3  3  1 3 1 1 | 0 3 1 1 1
------------------+-------+-------------+----------------------------+-------------------------+----------
.. x. ..    ..    |  2  0 | 96  *  *  * |  1  1  1  0  1  0  0  0  0 | 1 1 1  1  0  1  1 0 0 0 | 1 1 1 1 0
oo3oo3oo *b3oo&#x |  1  1 |  * 96  *  * |  0  0  0  1  2  1  0  0  0 | 0 0 0  2  1  2  1 0 0 0 | 0 2 1 1 0
.x .. ..    ..    |  0  2 |  *  * 48  * |  0  0  0  1  0  0  2  1  0 | 0 0 0  2  1  0  0 2 1 0 | 0 2 1 0 1
.. .. .x    ..    |  0  2 |  *  *  * 48 |  0  0  0  0  0  1  0  1  2 | 0 0 0  0  1  2  0 2 0 1 | 0 2 0 1 1
------------------+-------+-------------+----------------------------+-------------------------+----------
o.3x. ..    ..    |  3  0 |  3  0  0  0 | 32  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0 0 0 0 | 1 1 1 0 0
.. x.3o.    ..    |  3  0 |  3  0  0  0 |  * 32  *  *  *  *  *  *  * | 1 0 1  0  0  1  0 0 0 0 | 1 1 0 1 0
.. x. .. *b3o.    |  3  0 |  3  0  0  0 |  *  * 32  *  *  *  *  *  * | 0 1 1  0  0  0  1 0 0 0 | 1 0 1 1 0
ox .. ..    ..&#x |  1  2 |  0  2  1  0 |  *  *  * 48  *  *  *  *  * | 0 0 0  2  1  0  0 0 0 0 | 0 2 1 0 0
.. xo ..    ..&#x |  2  1 |  1  2  0  0 |  *  *  *  * 96  *  *  *  * | 0 0 0  1  0  1  1 0 0 0 | 0 1 1 1 0
.. .. ox    ..&#x |  1  2 |  0  2  0  1 |  *  *  *  *  * 48  *  *  * | 0 0 0  0  1  2  0 0 0 0 | 0 2 0 1 0
.x3.o ..    ..    |  0  3 |  0  0  3  0 |  *  *  *  *  *  * 32  *  * | 0 0 0  1  0  0  0 1 1 0 | 0 1 1 0 1
.x .. .x    ..    |  0  4 |  0  0  2  2 |  *  *  *  *  *  *  * 24  * | 0 0 0  0  1  0  0 2 0 0 | 0 2 0 0 1
.. .o3.x    ..    |  0  3 |  0  0  0  3 |  *  *  *  *  *  *  *  * 32 | 0 0 0  0  0  1  0 1 0 1 | 0 1 0 1 1
------------------+-------+-------------+----------------------------+-------------------------+----------
o.3x.3o.    ..      6  0 | 12  0  0  0 |  4  4  0  0  0  0  0  0  0 | 8 * *  *  *  *  * * * * | 1 1 0 0 0
o.3x. .. *b3o.      6  0 | 12  0  0  0 |  4  0  4  0  0  0  0  0  0 | * 8 *  *  *  *  * * * * | 1 0 1 0 0
.. x.3o. *b3o.      6  0 | 12  0  0  0 |  0  4  4  0  0  0  0  0  0 | * * 8  *  *  *  * * * * | 1 0 0 1 0
ox3xo ..    ..&#x   3  3 |  3  6  3  0 |  1  0  0  3  3  0  1  0  0 | * * * 32  *  *  * * * * | 0 1 1 0 0
ox .. ox    ..&#x   1  4 |  0  4  2  2 |  0  0  0  2  0  2  0  1  0 | * * *  * 24  *  * * * * | 0 2 0 0 0
.. xo3ox    ..&#x   3  3 |  3  6  0  3 |  0  1  0  0  3  3  0  0  1 | * * *  *  * 32  * * * * | 0 1 0 1 0
.. xo .. *b3oo&#x   3  1 |  3  3  0  0 |  0  0  1  0  3  0  0  0  0 | * * *  *  *  * 32 * * * | 0 0 1 1 0
.x3.o3.x    ..      0 12 |  0  0 12 12 |  0  0  0  0  0  0  4  6  4 | * * *  *  *  *  * 8 * * | 0 1 0 0 1
.x3.o .. *b3.o      0  4 |  0  0  6  0 |  0  0  0  0  0  0  4  0  0 | * * *  *  *  *  * * 8 * | 0 0 1 0 1
.. .o3.x *b3.o      0  4 |  0  0  0  6 |  0  0  0  0  0  0  0  0  4 | * * *  *  *  *  * * * 8 | 0 0 0 1 1
------------------+-------+-------------+----------------------------+-------------------------+----------
o.3x.3o. *b3o.     24  0 | 96  0  0  0 | 32 32 32  0  0  0  0  0  0 | 8 8 8  0  0  0  0 0 0 0 | 1 * * * *
ox3xo3ox    ..      6 12 | 12 24 12 12 |  4  4  0 12 12 12  4  6  4 | 1 0 0  4  6  4  0 1 0 0 | * 8 * * *
ox3xo .. *b3oo&#x   6  4 | 12 12  6  0 |  4  0  4  6 12  0  4  0  0 | 0 1 0  4  0  0  4 0 1 0 | * * 8 * *
.. xo3ox *b3oo&#x   6  4 | 12 12  0  6 |  0  4  4  0 12  6  0  0  4 | 0 0 1  0  0  4  4 0 0 1 | * * * 8 *
.x3.o3.x *b3.o      0 32 |  0  0 48 48 |  0  0  0  0  0  0 32 24 32 | 0 0 0  0  0  0  0 8 8 8 | * * * * 1

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