Acronym tutcupip
Name tuttip atop inverted tuttip,
tuta-prism,
medial segment of rittip
Circumradius sqrt(7)/2 = 1.322876
Lace city
in approx. ASCII-art
x3o x   x3x x        
                     
                     
                     
    u3o x   o3u x    
                     
                     
                     
        x3x x   o3x x
x3x3o o3x3x
           
           
           
           
           
           
x3x3o o3x3x
Face vector 48, 144, 164, 84, 18
Confer
uniform relative:
rittip  
general polytopal classes:
scaliform   segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xx ox3xx3xo&#x   → height = 1/sqrt(2) = 0.707107
(tuttip || inv tuttip)

o. o.3o.3o.    | 24  * |  1  2  1  2  0  0  0 |  2 1 1 2  2  1  2  2 0  0 0 0 | 1 2 1  1  2  2 1  1 2 0 0 0 | 1 1 1 2 1 0
.o .o3.o3.o    |  * 24 |  0  0  0  2  1  1  2 |  0 0 0 0  2  2  2  1 1  2 2 1 | 0 0 0  2  2  1 2  1 1 2 1 1 | 0 2 1 1 1 1
---------------+-------+----------------------+-------------------------------+-----------------------------+------------
x. .. .. ..    |  2  0 | 12  *  *  *  *  *  * |  2 1 0 0  2  0  0  0 0  0 0 0 | 1 2 0  1  2  2 0  0 0 0 0 0 | 1 1 1 2 0 0
.. .. x. ..    |  2  0 |  * 24  *  *  *  *  * |  1 0 1 1  0  0  1  0 0  0 0 0 | 1 1 1  0  1  0 1  0 1 0 0 0 | 1 1 0 1 1 0
.. .. .. x.    |  2  0 |  *  * 12  *  *  *  * |  0 1 0 2  0  0  0  2 0  0 0 0 | 0 2 1  0  0  2 0  1 2 0 0 0 | 1 0 1 2 1 0
oo oo3oo3oo&#x |  1  1 |  *  *  * 48  *  *  * |  0 0 0 0  1  1  1  1 0  0 0 0 | 0 0 0  1  1  1 1  1 1 0 0 0 | 0 1 1 1 1 0
.x .. .. ..    |  0  2 |  *  *  *  * 12  *  * |  0 0 0 0  2  0  0  0 1  2 0 0 | 0 0 0  2  2  1 0  0 0 2 1 0 | 0 2 1 1 0 1
.. .x .. ..    |  0  2 |  *  *  *  *  * 12  * |  0 0 0 0  0  2  0  0 1  0 2 0 | 0 0 0  2  0  0 2  1 0 2 0 1 | 0 2 1 0 1 1
.. .. .x ..    |  0  2 |  *  *  *  *  *  * 24 |  0 0 0 0  0  0  1  0 0  1 1 1 | 0 0 0  0  1  0 1  0 1 1 1 1 | 0 1 0 1 1 1
---------------+-------+----------------------+-------------------------------+-----------------------------+------------
x. .. x. ..    |  4  0 |  2  2  0  0  0  0  0 | 12 * * *  *  *  *  * *  * * * | 1 1 0  0  1  0 0  0 0 0 0 0 | 1 1 0 1 0 0
x. .. .. x.    |  4  0 |  2  0  2  0  0  0  0 |  * 6 * *  *  *  *  * *  * * * | 0 2 0  0  0  2 0  0 0 0 0 0 | 1 0 1 2 0 0
.. o.3x. ..    |  3  0 |  0  3  0  0  0  0  0 |  * * 8 *  *  *  *  * *  * * * | 1 0 1  0  0  0 1  0 0 0 0 0 | 1 1 0 0 1 0
.. .. x.3x.    |  6  0 |  0  3  3  0  0  0  0 |  * * * 8  *  *  *  * *  * * * | 0 1 1  0  0  0 0  0 1 0 0 0 | 1 0 0 1 1 0
xx .. .. ..&#x |  2  2 |  1  0  0  2  1  0  0 |  * * * * 24  *  *  * *  * * * | 0 0 0  1  1  1 0  0 0 0 0 0 | 0 1 1 1 0 0
.. ox .. ..&#x |  1  2 |  0  0  0  2  0  1  0 |  * * * *  * 24  *  * *  * * * | 0 0 0  1  0  0 1  1 0 0 0 0 | 0 1 1 0 1 0
.. .. xx ..&#x |  2  2 |  0  1  0  2  0  0  1 |  * * * *  *  * 24  * *  * * * | 0 0 0  0  1  0 1  0 1 0 0 0 | 0 1 0 1 1 0
.. .. .. xo&#x |  2  1 |  0  0  1  2  0  0  0 |  * * * *  *  *  * 24 *  * * * | 0 0 0  0  0  1 0  1 1 0 0 0 | 0 0 1 1 1 0
.x .x .. ..    |  0  4 |  0  0  0  0  2  2  0 |  * * * *  *  *  *  * 6  * * * | 0 0 0  2  0  0 0  0 0 2 0 0 | 0 2 1 0 0 1
.x .. .x ..    |  0  4 |  0  0  0  0  2  0  2 |  * * * *  *  *  *  * * 12 * * | 0 0 0  0  1  0 0  0 0 1 1 0 | 0 1 0 1 0 1
.. .x3.x ..    |  0  6 |  0  0  0  0  0  3  3 |  * * * *  *  *  *  * *  * 8 * | 0 0 0  0  0  0 1  0 0 1 0 1 | 0 1 0 0 1 1
.. .. .x3.o    |  0  3 |  0  0  0  0  0  0  3 |  * * * *  *  *  *  * *  * * 8 | 0 0 0  0  0  0 0  0 1 0 1 1 | 0 0 0 1 1 1
---------------+-------+----------------------+-------------------------------+-----------------------------+------------
x. o.3x. ..      6  0 |  3  6  0  0  0  0  0 |  3 0 2 0  0  0  0  0 0  0 0 0 | 4 * *  *  *  * *  * * * * * | 1 1 0 0 0 0
x. .. x.3x.     12  0 |  6  6  6  0  0  0  0 |  3 3 0 2  0  0  0  0 0  0 0 0 | * 4 *  *  *  * *  * * * * * | 1 0 0 1 0 0
.. o.3x.3x.     12  0 |  0 12  6  0  0  0  0 |  0 0 4 4  0  0  0  0 0  0 0 0 | * * 2  *  *  * *  * * * * * | 1 0 0 0 1 0
xx ox .. ..&#x   2  4 |  1  0  0  4  2  2  0 |  0 0 0 0  2  2  0  0 1  0 0 0 | * * * 12  *  * *  * * * * * | 0 1 1 0 0 0
xx .. xx ..&#x   4  4 |  2  2  0  4  2  0  2 |  1 0 0 0  2  0  2  0 0  1 0 0 | * * *  * 12  * *  * * * * * | 0 1 0 1 0 0
xx .. .. xo&#x   4  2 |  2  0  2  4  1  0  0 |  0 1 0 0  2  0  0  2 0  0 0 0 | * * *  *  * 12 *  * * * * * | 0 0 1 1 0 0
.. ox3xx ..&#x   3  6 |  0  3  0  6  0  3  3 |  0 0 1 0  0  3  3  0 0  0 1 0 | * * *  *  *  * 8  * * * * * | 0 1 0 0 1 0
.. ox .. xo&#x   2  2 |  0  0  1  4  0  1  0 |  0 0 0 0  0  2  0  2 0  0 0 0 | * * *  *  *  * * 12 * * * * | 0 0 1 0 1 0
.. .. xx3xo&#x   6  3 |  0  3  3  6  0  0  3 |  0 0 0 1  0  0  3  3 0  0 0 1 | * * *  *  *  * *  * 8 * * * | 0 0 0 1 1 0
.x .x3.x ..      0 12 |  0  0  0  0  6  6  6 |  0 0 0 0  0  0  0  0 3  3 2 0 | * * *  *  *  * *  * * 4 * * | 0 1 0 0 0 1
.x .. .x3.o      0  6 |  0  0  0  0  3  0  6 |  0 0 0 0  0  0  0  0 0  3 0 2 | * * *  *  *  * *  * * * 4 * | 0 0 0 1 0 1
.. .x3.x3.o      0 12 |  0  0  0  0  0  6 12 |  0 0 0 0  0  0  0  0 0  0 4 4 | * * *  *  *  * *  * * * * 2 | 0 0 0 0 1 1
---------------+-------+----------------------+-------------------------------+-----------------------------+------------
x. o.3x.3x.     24  0 | 12 24 12  0  0  0  0 | 12 6 8 8  0  0  0  0 0  0 0 0 | 4 4 2  0  0  0 0  0 0 0 0 0 | 1 * * * * *
xx ox3xx ..&#x   6 12 |  3  6  0 12  6  6  6 |  3 0 2 0  6  6  6  0 3  3 2 0 | 1 0 0  3  3  0 2  0 0 1 0 0 | * 4 * * * *
xx ox .. xo&#x   4  4 |  2  0  2  8  2  2  0 |  0 1 0 0  4  4  0  4 1  0 0 0 | 0 0 0  2  0  2 0  2 0 0 0 0 | * * 6 * * *
xx .. xx3xo&#x  12  6 |  6  6  6 12  3  0  6 |  3 3 0 2  6  0  6  6 0  3 0 2 | 0 1 0  0  3  3 0  0 2 0 1 0 | * * * 4 * *
.. ox3xx3xo&#x  12 12 |  0 12  6 24  0  6 12 |  0 0 4 4  0 12 12 12 0  0 4 4 | 0 0 1  0  0  0 4  6 4 0 0 1 | * * * * 2 *
.x .x3.x3.o      0 24 |  0  0  0  0 12 12 24 |  0 0 0 0  0  0  0  0 6 12 8 8 | 0 0 0  0  0  0 0  0 0 4 4 2 | * * * * * 1

x s4o3x2s = x2s4o3x2s
(tuta || tuta)

demi( . . . . . ) | 48 |  1  2  1  2 |  2  1  1  2  2  2  3 | 1  2 1  1 2  3  3 | 1 1 1 3
------------------+----+-------------+----------------------+-------------------+--------
demi( x . . . . ) |  2 | 24  *  *  * |  2  0  1  2  0  0  0 | 1  2 0  0 2  3  0 | 1 1 0 3
demi( . . . x . ) |  2 |  * 48  *  * |  1  1  0  0  1  1  0 | 1  1 1  0 1  0  2 | 1 0 1 2
      . s4o . .   |  2 |  *  * 24  * |  0  0  1  0  0  2  2 | 0  0 1  1 2  2  2 | 1 1 1 2
      . s . 2 s   |  2 |  *  *  * 48 |  0  0  0  1  1  0  2 | 0  1 0  1 0  2  2 | 0 1 1 2
------------------+----+-------------+----------------------+-------------------+--------
demi( x . . x . ) |  4 |  2  2  0  0 | 24  *  *  *  *  *  * | 1  1 0  0 1  0  0 | 1 0 0 2
demi( . . o3x . ) |  3 |  0  3  0  0 |  * 16  *  *  *  *  * | 1  0 1  0 0  0  1 | 1 0 1 1
      x s4o . .   |  4 |  2  0  2  0 |  *  * 12  *  *  *  * | 0  0 0  0 2  2  0 | 1 1 0 2
      x s . 2 s   |  4 |  2  0  0  2 |  *  *  * 24  *  *  * | 0  1 0  0 0  2  0 | 0 1 0 2
      . s 2 x2s   |  4 |  0  2  0  2 |  *  *  *  * 24  *  * | 0  1 0  0 0  0  2 | 0 0 1 2
sefa( . s4o3x . ) |  6 |  0  3  3  0 |  *  *  *  *  * 16  * | 0  0 1  0 1  0  1 | 1 0 1 1
sefa( . s4o 2 s ) |  3 |  0  0  1  2 |  *  *  *  *  *  * 48 | 0  0 0  1 0  1  1 | 0 1 1 1
------------------+----+-------------+----------------------+-------------------+--------
demi( x . o3x . )   6 |  3  6  0  0 |  3  2  0  0  0  0  0 | 8  * *  * *  *  * | 1 0 0 1
      x s 2 x2s     8 |  4  4  0  4 |  2  0  0  2  2  0  0 | * 12 *  * *  *  * | 0 0 0 2
      . s4o3x .    12 |  0 12  6  0 |  0  4  0  0  0  4  0 | *  * 4  * *  *  * | 1 0 1 0
      . s4o 2 s     4 |  0  0  2  4 |  0  0  0  0  0  0  4 | *  * * 12 *  *  * | 0 1 1 0
sefa( x s4o3x . )  12 |  6  6  6  0 |  3  0  3  0  0  2  0 | *  * *  * 8  *  * | 1 0 0 1
sefa( x s4o 2 s )   6 |  3  0  2  4 |  0  0  1  2  0  0  2 | *  * *  * * 24  * | 0 1 0 1
sefa( . s4o3x2s )   9 |  0  6  3  6 |  0  1  0  0  3  1  3 | *  * *  * *  * 16 | 0 0 1 1
------------------+----+-------------+----------------------+-------------------+--------
      x s4o3x .    24 | 12 24 12  0 | 12  8  6  0  0  8  0 | 4  0 2  0 4  0  0 | 2 * * *
      x s4o 2 s     8 |  4  0  4  8 |  0  0  2  4  0  0  8 | 0  0 0  2 0  4  0 | * 6 * *
      . s4o3x2s    24 |  0 24 12 24 |  0  8  0  0 12  8 24 | 0  0 2  6 0  0  8 | * * 2 *
sefa( x s4o3x2s )  18 |  9 12  6 12 |  6  2  3  6  6  2  6 | 1  3 0  0 1  3  2 | * * * 8

starting figure: x x4o3x x

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