Acronym rapatut (alt.: tetoct tuttric)
Name rap atop tut,
(tet,oct,tut)-trigonic
Circumradius sqrt(17/12) = 1.190238
Lace city
in approx. ASCII-art
     O     
           
           
           
t         T

where:
t = x3o3o (tet)
O = o3x3o (oct)
T = x3x3o (tut)
Confer
uniform relative:
spix  
general polytopal classes:
segmentotera   lace simplices  

This polyteron occurs as a wedge within spix.


Incidence matrix according to Dynkin symbol

ooo3oxx3xox&#x   → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569
                   height(1,3) = 1/sqrt(2) = 0.707107
                   height(12,3) = sqrt(3/5) = 0.774597
(rap || tut)

o..3o..3o..    | 4 *  * | 3  3  3  0  0  0 0 | 3  3 3  3  3 3 0 0  0 0 0 0 | 1 1 3  3 3 1 3 0 0 0 0 | 1 1 3 1 0
.o.3.o.3.o.    | * 6  * | 0  2  0  4  2  0 0 | 0  4 1  2  0 0 2 2  4 1 0 0 | 0 2 2  4 1 0 0 1 2 2 0 | 1 2 2 0 1
..o3..o3..o    | * * 12 | 0  0  1  0  1  2 1 | 0  0 0  1  2 1 0 0  2 1 1 2 | 0 0 0  2 1 1 2 0 1 2 1 | 0 1 2 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
... ... x..    | 2 0  0 | 6  *  *  *  *  * * | 2  0 1  0  0 1 0 0  0 0 0 0 | 1 0 2  0 1 0 2 0 0 0 0 | 1 0 2 1 0
oo.3oo.3oo.&#x | 1 1  0 | * 12  *  *  *  * * | 0  2 1  1  0 0 0 0  0 0 0 0 | 0 1 2  2 1 0 0 0 0 0 0 | 1 1 2 0 0
o.o3o.o3o.o&#x | 1 0  1 | *  * 12  *  *  * * | 0  0 0  1  2 1 0 0  0 0 0 0 | 0 0 0  2 1 1 2 0 0 0 0 | 0 1 2 1 0
... .x. ...    | 0 2  0 | *  *  * 12  *  * * | 0  1 0  0  0 0 1 1  1 0 0 0 | 0 1 1  1 0 0 0 1 1 1 0 | 1 1 1 0 1
.oo3.oo3.oo&#x | 0 1  1 | *  *  *  * 12  * * | 0  0 0  1  0 0 0 0  2 1 0 0 | 0 0 0  2 1 0 0 0 1 2 0 | 0 1 2 0 1
... ..x ...    | 0 0  2 | *  *  *  *  * 12 * | 0  0 0  0  1 0 0 0  1 0 1 1 | 0 0 0  1 0 1 1 0 1 1 1 | 0 1 1 1 1
... ... ..x    | 0 0  2 | *  *  *  *  *  * 6 | 0  0 0  0  0 1 0 0  0 1 0 2 | 0 0 0  0 1 0 2 0 0 2 1 | 0 0 2 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
... o..3x..    | 3 0  0 | 3  0  0  0  0  0 0 | 4  * *  *  * * * *  * * * * | 1 0 1  0 0 0 1 0 0 0 0 | 1 0 1 1 0
... ox. ...&#x | 1 2  0 | 0  2  0  1  0  0 0 | * 12 *  *  * * * *  * * * * | 0 1 1  1 0 0 0 0 0 0 0 | 1 1 1 0 0
... ... xo.&#x | 2 1  0 | 1  2  0  0  0  0 0 | *  * 6  *  * * * *  * * * * | 0 0 2  0 1 0 0 0 0 0 0 | 1 0 2 0 0
ooo3ooo3ooo&#x | 1 1  1 | 0  1  1  0  1  0 0 | *  * * 12  * * * *  * * * * | 0 0 0  2 1 0 0 0 0 0 0 | 0 1 2 0 0
... o.x ...&#x | 1 0  2 | 0  0  2  0  0  1 0 | *  * *  * 12 * * *  * * * * | 0 0 0  1 0 1 1 0 0 0 0 | 0 1 1 1 0
... ... x.x&#x | 2 0  2 | 1  0  2  0  0  0 1 | *  * *  *  * 6 * *  * * * * | 0 0 0  0 1 0 2 0 0 0 0 | 0 0 2 1 0
.o.3.x. ...    | 0 3  0 | 0  0  0  3  0  0 0 | *  * *  *  * * 4 *  * * * * | 0 1 0  0 0 0 0 1 1 0 0 | 1 1 0 0 1
... .x.3.o.    | 0 3  0 | 0  0  0  3  0  0 0 | *  * *  *  * * * 4  * * * * | 0 0 1  0 0 0 0 1 0 1 0 | 1 0 1 0 1
... .xx ...&#x | 0 2  2 | 0  0  0  1  2  1 0 | *  * *  *  * * * * 12 * * * | 0 0 0  1 0 0 0 0 1 1 0 | 0 1 1 0 1
... ... .ox&#x | 0 1  2 | 0  0  0  0  2  0 1 | *  * *  *  * * * *  * 6 * * | 0 0 0  0 1 0 0 0 0 2 0 | 0 0 2 0 1
..o3..x ...    | 0 0  3 | 0  0  0  0  0  3 0 | *  * *  *  * * * *  * * 4 * | 0 0 0  0 0 1 0 0 1 0 1 | 0 1 0 1 1
... ..x3..x    | 0 0  6 | 0  0  0  0  0  3 3 | *  * *  *  * * * *  * * * 4 | 0 0 0  0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
o..3o..3x..     4 0  0 | 6  0  0  0  0  0 0 | 4  0 0  0  0 0 0 0  0 0 0 0 | 1 * *  * * * * * * * * | 1 0 0 1 0
oo.3ox. ...&#x  1 3  0 | 0  3  0  3  0  0 0 | 0  3 0  0  0 0 1 0  0 0 0 0 | * 4 *  * * * * * * * * | 1 1 0 0 0
... ox.3xo.&#x  3 3  0 | 3  6  0  3  0  0 0 | 1  3 3  0  0 0 0 1  0 0 0 0 | * * 4  * * * * * * * * | 1 0 1 0 0
... oxx ...&#x  1 2  2 | 0  2  2  1  2  1 0 | 0  1 0  2  1 0 0 0  1 0 0 0 | * * * 12 * * * * * * * | 0 1 1 0 0
... ... xox&#x  2 1  2 | 1  2  2  0  2  0 1 | 0  0 1  2  0 1 0 0  0 1 0 0 | * * *  * 6 * * * * * * | 0 0 2 0 0
o.o3o.x ...&#x  1 0  3 | 0  0  3  0  0  3 0 | 0  0 0  0  3 0 0 0  0 0 1 0 | * * *  * * 4 * * * * * | 0 1 0 1 0
... o.x3x.x&#x  3 0  6 | 3  0  6  0  0  3 3 | 1  0 0  0  3 3 0 0  0 0 0 1 | * * *  * * * 4 * * * * | 0 0 1 1 0
.o.3.x.3.o.     0 6  0 | 0  0  0 12  0  0 0 | 0  0 0  0  0 0 4 4  0 0 0 0 | * * *  * * * * 1 * * * | 1 0 0 0 1
.oo3.xx ...&#x  0 3  3 | 0  0  0  3  3  3 0 | 0  0 0  0  0 0 1 0  3 0 1 0 | * * *  * * * * * 4 * * | 0 1 0 0 1
... .xx3.ox&#x  0 3  6 | 0  0  0  3  6  3 3 | 0  0 0  0  0 0 0 1  3 3 0 1 | * * *  * * * * * * 4 * | 0 0 1 0 1
..o3..x3..x     0 0 12 | 0  0  0  0  0 12 6 | 0  0 0  0  0 0 0 0  0 0 4 4 | * * *  * * * * * * * 1 | 0 0 0 1 1
---------------+--------+--------------------+-----------------------------+------------------------+----------
oo.3ox.3xo.&#x  4 6  0 | 6 12  0 12  0  0 0 | 4 12 6  0  0 0 4 4  0 0 0 0 | 1 4 4  0 0 0 0 1 0 0 0 | 1 * * * *
ooo3oxx ...&#x  1 3  3 | 0  3  3  3  3  3 0 | 0  3 0  3  3 0 1 0  3 0 1 0 | 0 1 0  3 0 1 0 0 1 0 0 | * 4 * * *
... oxx3xox&#x  3 3  6 | 3  6  6  3  6  3 3 | 1  3 3  6  3 3 0 1  3 3 0 1 | 0 0 1  3 3 0 1 0 0 1 0 | * * 4 * *
o.o3o.x3x.x&#x  4 0 12 | 6  0 12  0  0 12 6 | 4  0 0  0 12 6 0 0  0 0 4 4 | 1 0 0  0 0 4 4 0 0 0 1 | * * * 1 *
.oo3.xx3.ox&#x  0 6 12 | 0  0  0 12 12 12 6 | 0  0 0  0  0 0 4 4 12 6 4 4 | 0 0 0  0 0 0 0 1 4 4 1 | * * * * 1

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