Acronym hextum
Name hex-based tutsatope,
hex-based tutism
Circumradius sqrt(5/2) = 1.581139
Lace city
in approx. ASCII-art
       o3o4o  x3o4o  o3o4o       
                                 
                                 
                                 
o3o4o         u3o4o         o3o4o
                                 
                                 
                                 
x3o4o  u3o4o  x3x4o  u3o4o  x3o4o
Coordinates (sqrt(2), 1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign, but last coordinate not negative
Confer
uniform relative:
tot  

Incidence matrix according to Dynkin symbol

xux3oox3ooo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(hex || pseudo u-hex || thex)

o..3o..3o..4o..     | 8 *  * |  6 1  0  0  0 | 12  6  0  0  0 |  8 12  0  0 0 | 1  8 0 0
.o.3.o.3.o.4.o.     | * 8  * |  0 1  6  0  0 |  0  6 12  0  0 |  0 12  8  0 0 | 0  8 1 0
..o3..o3..o4..o     | * * 48 |  0 0  1  1  4 |  0  1  4  4  4 |  0  4  4  4 1 | 0  4 1 1
--------------------+--------+---------------+----------------+---------------+---------
x.. ... ... ...     | 2 0  0 | 24 *  *  *  * |  4  1  0  0  0 |  4  4  0  0 0 | 1  4 0 0
oo.3oo.3oo.4oo.&#x  | 1 1  0 |  * 8  *  *  *   0  6  0  0  0 |  0 12  0  0 0 | 0  8 0 0
.oo3.oo3.oo4.oo&#x  | 0 1  1 |  * * 48  *  * |  0  1  4  0  0 |  0  4  4  0 0 | 0  4 1 0
..x ... ... ...     | 0 0  2 |  * *  * 24  *   0  1  0  4  0 |  0  4  0  4 0 | 0  4 0 1
... ..x ... ...     | 0 0  2 |  * *  *  * 96 |  0  0  1  1  2 |  0  1  2  2 1 | 0  2 1 1
--------------------+--------+---------------+----------------+---------------+---------
x..3o.. ... ...     | 3 0  0 |  3 0  0  0  0 | 32  *  *  *  * |  2  1  0  0 0 | 1  2 0 0
xux ... ... ...&#xt | 2 2  2 |  1 2  2  1  0 |  * 24  *  *  * |  0  4  0  0 0 | 0  4 0 0
... .ox ... ...&#x  | 0 1  2 |  0 0  2  0  1 |  *  * 96  *  * |  0  1  2  0 0 | 0  2 1 0
..x3..x ... ...     | 0 0  6 |  0 0  0  3  3 |  *  *  * 32  * |  0  1  0  2 0 | 0  2 0 1
... ..x3..o ...     | 0 0  3 |  0 0  0  0  3 |  *  *  *  * 64 |  0  0  1  1 1 | 0  1 1 1
--------------------+--------+---------------+----------------+---------------+---------
x..3o..3o.. ...      4 0  0 |  6 0  0  0  0 |  4  0  0  0  0 | 16  *  *  * * | 1  1 0 0
xux3oox ... ...&#xt  3 3  6 |  3 3  6  3  3 |  1  3  3  1  0 |  * 32  *  * * | 0  2 0 0
... .ox3.oo ...&#x   0 1  3 |  0 0  3  0  3 |  0  0  3  0  1 |  *  * 64  * * | 0  1 1 0
..x3..x3..o ...      0 0 12 |  0 0  0  6 12 |  0  0  0  4  4 |  *  *  * 16 * | 0  1 0 1
... ..x3..o4..o      0 0  6 |  0 0  0  0 12 |  0  0  0  0  8 |  *  *  *  * 8 | 0  0 1 1
--------------------+--------+---------------+----------------+---------------+---------
x..3o..3o..4o..      8 0  0 | 24 0  0  0  0 | 32  0  0  0  0 | 16  0  0  0 0 | 1  * * *
xux3oox3ooo ...&#xt  4 4 12 |  6 4 12  6 12 |  4  6 12  4  4 |  1  4  4  1 0 | * 16 * *
... .ox3.oo4.oo&#x   0 1  6 |  0 0  6  0 12 |  0  0 12  0  8 |  0  0  8  0 1 | *  * 8 *
..x3..o3..o4..o      0 0 48 |  0 0  0 24 96 |  0  0  0 32 64 |  0  0  0 16 8 | *  * * 1

xux3xoo3ooo *b3ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(hex || pseudo u-hex || thex)

o..3o..3o.. *b3o..     | 8 *  * |  6 1  0  0  0 | 12  6  0  0  0  0 | 4 4 12  0  0 0 0 0 | 1 4 4 0 0
.o.3.o.3.o. *b3.o.     | * 8  * |  0 1  6  0  0 |  0  6 12  0  0  0 | 0 0 12  4  4 0 0 0 | 0 4 4 1 0
..o3..o3..o *b3..o     | * * 48 |  0 0  1  1  4 |  0  1  4  4  2  2 | 0 0  4  2  2 2 2 1 | 0 2 2 1 1
-----------------------+--------+---------------+-------------------+--------------------+----------
x.. ... ...    ...     | 2 0  0 | 24 *  *  *  * |  4  1  0  0  0  0 | 2 2  4  0  0 0 0 0 | 1 2 2 0 0
oo.3oo.3oo. *b3oo.&#x  | 1 1  0 |  * 8  *  *  *   0  6  0  0  0  0 | 0 0 12  0  0 0 0 0 | 0 4 4 0 0
.oo3.oo3.oo *b3.oo&#x  | 0 1  1 |  * * 48  *  * |  0  1  4  0  0  0 | 0 0  4  2  2 0 0 0 | 0 2 2 1 0
..x ... ...    ...     | 0 0  2 |  * *  * 24  *   0  1  0  4  0  0 | 0 0  4  0  0 2 2 0 | 0 2 2 0 1
... ..x ...    ...     | 0 0  2 |  * *  *  * 96 |  0  0  1  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
-----------------------+--------+---------------+-------------------+--------------------+----------
x..3o.. ...    ...     | 3 0  0 |  3 0  0  0  0 | 32  *  *  *  *  * | 1 1  1  0  0 0 0 0 | 1 1 1 0 0
xux ... ...    ...&#xt | 2 2  2 |  1 2  2  1  0 |  * 24  *  *  *  * | 0 0  4  0  0 0 0 0 | 0 2 2 0 0
... .ox ...    ...&#x  | 0 1  2 |  0 0  2  0  1 |  *  * 96  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
..x3..x ...    ...     | 0 0  6 |  0 0  0  3  3 |  *  *  * 32  *  * | 0 0  1  0  0 1 1 0 | 0 1 1 0 1
... ..x3..o    ...     | 0 0  3 |  0 0  0  0  3 |  *  *  *  * 32  * | 0 0  0  1  0 1 0 1 | 0 1 0 1 1
... ..x ... *b3..o     | 0 0  3 |  0 0  0  0  3 |  *  *  *  *  * 32 | 0 0  0  0  1 0 1 1 | 0 0 1 1 1
-----------------------+--------+---------------+-------------------+--------------------+----------
x..3o..3o..    ...      4 0  0 |  6 0  0  0  0 |  4  0  0  0  0  0 | 8 *  *  *  * * * * | 1 1 0 0 0
x..3o.. ... *b3..o      4 0  0 |  6 0  0  0  0 |  4  0  0  0  0  0 | * 8  *  *  * * * * | 1 0 1 0 0
xux3oox ...    ...&#xt  3 3  6 |  3 3  6  3  3 |  1  3  3  1  0  0 | * * 32  *  * * * * | 0 1 1 0 0
... .ox3.oo    ...&#x   0 1  3 |  0 0  3  0  3 |  0  0  3  0  1  0 | * *  * 32  * * * * | 0 1 0 1 0
... .ox ... *b3.oo&#x   0 1  3 |  0 0  3  0  3 |  0  0  3  0  0  1 | * *  *  * 32 * * * | 0 0 1 1 0
..x3..x3..o    ...      0 0 12 |  0 0  0  6 12 |  0  0  0  4  4  0 | * *  *  *  * 8 * * | 0 1 0 0 1
..x3..x ... *b3..o      0 0 12 |  0 0  0  6 12 |  0  0  0  4  0  4 | * *  *  *  * * 8 * | 0 0 1 0 1
... ..x3..o *b3..o      0 0  6 |  0 0  0  0 12 |  0  0  0  0  4  4 | * *  *  *  * * * 8 | 0 0 0 1 1
-----------------------+--------+---------------+-------------------+--------------------+----------
x..3o..3o.. *b3..o      8 0  0 | 24 0  0  0  0 | 32  0  0  0  0  0 | 8 8  0  0  0 0 0 0 | 1 * * * *
xux3oox3ooo    ...&#xt  4 4 12 |  6 4 12  6 12 |  4  6 12  4  4  0 | 1 0  4  4  0 1 0 0 | * 8 * * *
xux3oox ... *b3ooo&#xt  4 4 12 |  6 4 12  6 12 |  4  6 12  4  0  4 | 0 1  4  0  4 0 1 0 | * * 8 * *
... .ox3.oo *b3.oo&#x   0 1  6 |  0 0  6  0 12 |  0  0 12  0  4  4 | 0 0  0  4  4 0 0 1 | * * * 8 *
..x3..x3..o *b3..o      0 0 48 |  0 0  0 24 96 |  0  0  0 32 32 32 | 0 0  0  0  0 8 8 8 | * * * * 1

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