Acronym hextum
Name hex-based tutsatope,
hex-based tutism,
hex-first rotunda of tot,
truncation of hexpy
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
Face vector 64, 200, 248, 136, 26
Confer
uniform relative:
tot  
general polytopal classes:
tutsatopes  

It is quite remarkable that hexpy allows for some of the same operations as regulars do: this polyteron is nothing but the truncation operation being applied to it.


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  {6}
... .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  {6}
... ..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


xux3oox3ooo *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  {6}
... .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  {6}
... ..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


trunc( xoo3ooo3oxo&#x )

trops( x.. ... ...    ) & | 24  * * * |  1  0 0  2  2  0  1  0  0  0 | 2  2  1  0 1  2 0  1  2 0  2  0  0 | 1 2 1 2  2 1 1 0  2 0 0  1 0 | 1 1 2 1 1 0
trops( oo.3oo.3oo.&#x )   |  * 24 * * |  0  1 0  0  2  2  0  0  1  0 | 0  4  0  1 0  1 1  2  0 0  2  2  0 | 0 2 2 0  4 1 0 0  1 1 0  2 0 | 1 0 2 2 1 0
tropA( o.o3o.o3o.o&#x ) & |  *  * 8 * |  0  0 1  0  0  0  3  0  3  0 | 0  0  3  3 0  0 0  0  3 0  6  3  0 | 0 0 0 3  9 0 1 0  3 1 0  3 0 | 0 1 4 3 1 0
tropB( o.o3o.o3o.o&#x ) & |  *  * * 8 |  0  0 1  0  0  0  0  3  0  3 | 0  0  3  3 0  0 0  0  0 3  0  0  9 | 0 0 0 3  9 0 0 1  0 0 4  0 3 | 0 1 4 3 0 1
--------------------------+-----------+------------------------------+------------------------------------+------------------------------+------------
trunc( x.. ... ...    ) & |  2  0 0 0 | 12  * *  *  *  *  *  *  *  * ♦ 2  2  1  0 0  0 0  0  0 0  0  0  0 | 1 2 1 2  2 0 0 0  0 0 0  0 0 | 1 1 2 1 0 0
trunc( oo.3oo.3oo.&#x )   |  0  2 0 0 |  * 12 *  *  *  *  *  *  *  * ♦ 0  4  0  1 0  0 0  0  0 0  0  0  0 | 0 2 2 0  4 0 0 0  0 0 0  0 0 | 1 0 2 2 0 0
trunc( o.o3o.o3o.o&#x ) & |  0  0 1 1 |  *  * 8  *  *  *  *  *  *  * ♦ 0  0  3  3 0  0 0  0  0 0  0  0  0 | 0 0 0 3  9 0 0 0  0 0 0  0 0 | 0 1 4 3 0 0
verf(  x..3o.. ...    ) & |  2  0 0 0 |  *  * * 24  *  *  *  *  *  * | 1  0  0  0 1  1 0  0  1 0  0  0  0 | 1 1 0 1  0 1 1 0  1 0 0  0 0 | 1 1 1 0 1 0
verfA( xo. ... ...&#x ) & |  1  1 0 0 |  *  * *  * 48  *  *  *  *  * | 0  1  0  0 0  1 0  1  0 0  1  0  0 | 0 1 1 0  1 1 0 0  1 0 0  1 0 | 1 0 1 1 1 0
verfB( xo. ... ...&#x ) & |  0  2 0 0 |  *  * *  *  * 24  *  *  *  * | 0  1  0  0 0  0 1  1  0 0  0  1  0 | 0 1 1 0  1 1 0 0  0 1 0  1 0 | 1 0 1 1 1 0
verfA( x.o ... ...&#x ) & |  1  0 1 0 |  *  * *  *  *  * 24  *  *  * | 0  0  1  0 0  0 0  0  2 0  2  0  0 | 0 0 0 2  2 0 1 0  2 0 0  1 0 | 0 1 2 1 1 0
verfB( x.o ... ...&#x ) & |  0  0 0 2 |  *  * *  *  *  *  * 12  *  * | 0  0  1  0 0  0 0  0  0 2  0  0  2 | 0 0 0 2  2 0 0 1  0 0 2  0 1 | 0 1 2 1 0 1
verfA( ooo3ooo3ooo&#x )   |  0  1 1 0 |  *  * *  *  *  *  *  * 24  * | 0  0  0  1 0  0 0  0  0 0  2  2  0 | 0 0 0 0  4 0 0 0  1 1 0  2 0 | 0 0 2 2 1 0
verfB( ooo3ooo3ooo&#x )   |  0  0 0 2 |  *  * *  *  *  *  *  *  * 12 | 0  0  0  1 0  0 0  0  0 0  0  0  4 | 0 0 0 0  4 0 0 0  0 0 2  0 2 | 0 0 2 2 0 1
--------------------------+-----------+------------------------------+------------------------------------+------------------------------+------------
trunc( x..3o.. ...    ) & |  6  0 0 0 |  3  0 0  3  0  0  0  0  0  0 | 8  *  *  * *  * *  *  * *  *  *  * | 1 1 0 1  0 0 0 0  0 0 0  0 0 | 1 1 1 0 0 0  {6}
trunc( xo. ... ...&#x ) & |  2  4 0 0 |  1  2 0  0  2  1  0  0  0  0 | * 24  *  * *  * *  *  * *  *  *  * | 0 1 1 0  1 0 0 0  0 0 0  0 0 | 1 0 1 1 0 0  {6}
trunc( x.o ... ...&#x ) & |  2  0 2 2 |  1  0 2  0  0  0  2  1  0  0 | *  * 12  * *  * *  *  * *  *  *  * | 0 0 0 2  2 0 0 0  0 0 0  0 0 | 0 1 2 1 0 0  {6}
trunc( ooo3ooo3ooo&#x )   |  0  2 2 2 |  0  1 2  0  0  0  0  0  2  1 | *  *  * 12 *  * *  *  * *  *  *  * | 0 0 0 0  4 0 0 0  0 0 0  0 0 | 0 0 2 2 0 0  {6}
verf(  x..3o..3o..    ) & |  3  0 0 0 |  0  0 0  3  0  0  0  0  0  0 | *  *  *  * 8  * *  *  * *  *  *  * | 1 0 0 0  0 1 1 0  0 0 0  0 0 | 1 1 0 0 1 0
verfA( xo.3oo. ...&#x ) & |  2  1 0 0 |  0  0 0  1  2  0  0  0  0  0 | *  *  *  * * 24 *  *  * *  *  *  * | 0 1 0 0  0 1 0 0  1 0 0  0 0 | 1 0 1 0 1 0
verfB( xo.3oo. ...&#x ) & |  0  3 0 0 |  0  0 0  0  0  3  0  0  0  0 | *  *  *  * *  * 8  *  * *  *  *  * | 0 1 0 0  0 1 0 0  0 1 0  0 0 | 1 0 1 0 1 0
verf(  xo. ... ox.&#x )   |  1  2 0 0 |  0  0 0  0  2  1  0  0  0  0 | *  *  *  * *  * * 24  * *  *  *  * | 0 0 1 0  0 1 0 0  0 0 0  1 0 | 1 0 0 1 1 0
verfA( x.o3o.o ...&#x ) & |  2  0 1 0 |  0  0 0  1  0  0  2  0  0  0 | *  *  *  * *  * *  * 24 *  *  *  * | 0 0 0 1  0 0 1 0  1 0 0  0 0 | 0 1 1 0 1 0
verfB( x.o3o.o ...&#x ) & |  0  0 0 3 |  0  0 0  0  0  0  0  3  0  0 | *  *  *  * *  * *  *  * 8  *  *  * | 0 0 0 1  0 0 0 1  0 0 1  0 0 | 0 1 1 0 0 1
verfA( xoo ... ...&#x ) & |  1  1 1 0 |  0  0 0  0  1  0  1  0  1  0 | *  *  *  * *  * *  *  * * 48  *  * | 0 0 0 0  1 0 0 0  1 0 0  1 0 | 0 0 1 1 1 0
verfB( xoo ... ...&#x ) & |  0  2 1 0 |  0  0 0  0  0  1  0  0  2  0 | *  *  *  * *  * *  *  * *  * 24  * | 0 0 0 0  1 0 0 0  0 1 0  1 0 | 0 0 1 1 1 0
verfC( xoo ... ...&#x ) & |  0  0 0 3 |  0  0 0  0  0  0  0  1  0  2 | *  *  *  * *  * *  *  * *  *  * 24 | 0 0 0 0  1 0 0 0  0 0 1  0 1 | 0 0 1 1 0 1
--------------------------+-----------+------------------------------+------------------------------------+------------------------------+------------
trunc( x..3o..3o..    ) & ♦ 12  0 0 0 |  6  0 0 12  0  0  0  0  0  0 | 4  0  0  0 4  0 0  0  0 0  0  0  0 | 2 * * *  * * * *  * * *  * * | 1 1 0 0 0 0
trunc( xo.3oo. ...&#x ) & ♦  6  6 0 0 |  3  3 0  3  6  3  0  0  0  0 | 1  3  0  0 0  3 1  0  0 0  0  0  0 | * 8 * *  * * * *  * * *  * * | 1 0 1 0 0 0
trunc( xo. ... ox.&#x )   ♦  4  8 0 0 |  2  4 0  0  8  4  0  0  0  0 | 0  4  0  0 0  0 0  4  0 0  0  0  0 | * * 6 *  * * * *  * * *  * * | 1 0 0 1 0 0
trunc( x.o3o.o ...&#x ) & ♦  6  0 3 3 |  3  0 3  3  0  0  6  3  0  0 | 1  0  3  0 0  0 0  0  3 1  0  0  0 | * * * 8  * * * *  * * *  * * | 0 1 1 0 0 0
trunc( xoo ... ...&#x ) & ♦  2  4 3 3 |  1  2 3  0  2  1  2  1  4  2 | 0  1  1  2 0  0 0  0  0 0  2  1  1 | * * * * 24 * * *  * * *  * * | 0 0 1 1 0 0
verf(  xo.3oo.3ox.&#x )   ♦  3  3 0 0 |  0  0 0  3  6  3  0  0  0  0 | 0  0  0  0 1  3 1  3  0 0  0  0  0 | * * * *  * 8 * *  * * *  * * | 1 0 0 0 1 0
verfA( x.o3o.o3o.o&#x ) & ♦  3  0 1 0 |  0  0 0  3  0  0  3  0  0  0 | 0  0  0  0 1  0 0  0  3 0  0  0  0 | * * * *  * * 8 *  * * *  * * | 0 1 0 0 1 0
verfB( x.o3o.o3o.o&#x ) & ♦  0  0 0 4 |  0  0 0  0  0  0  0  6  0  0 | 0  0  0  0 0  0 0  0  0 4  0  0  0 | * * * *  * * * 2  * * *  * * | 0 1 0 0 0 1
verfA( xoo3ooo ...&#x ) & ♦  2  1 1 0 |  0  0 0  1  2  0  2  0  1  0 | 0  0  0  0 0  1 0  0  1 0  2  0  0 | * * * *  * * * * 24 * *  * * | 0 0 1 0 1 0
verfB( xoo3ooo ...&#x ) & ♦  0  3 1 0 |  0  0 0  0  0  3  0  0  3  0 | 0  0  0  0 0  0 1  0  0 0  0  3  0 | * * * *  * * * *  * 8 *  * * | 0 0 1 0 1 0
verfC( xoo3ooo ...&#x ) & ♦  0  0 0 4 |  0  0 0  0  0  0  0  3  0  3 | 0  0  0  0 0  0 0  0  0 1  0  0  3 | * * * *  * * * *  * * 8  * * | 0 0 1 0 0 1
verfA( xoo ... oxo&#x )   ♦  1  2 1 0 |  0  0 0  0  2  1  1  0  2  0 | 0  0  0  0 0  0 0  1  0 0  2  1  0 | * * * *  * * * *  * * * 24 * | 0 0 0 1 1 0
verfB( xoo ... oxo&#x )   ♦  0  0 0 4 |  0  0 0  0  0  0  0  2  0  4 | 0  0  0  0 0  0 0  0  0 0  0  0  4 | * * * *  * * * *  * * *  * 6 | 0 0 0 1 0 1
--------------------------+-----------+------------------------------+------------------------------------+------------------------------+------------
trunc( xo.3oo.3ox.&#x )   ♦ 24 24 0 0 | 12 12 0 24 48 24  0  0  0  0 | 8 24  0  0 8 24 8 24  0 0  0  0  0 | 2 8 6 0  0 8 0 0  0 0 0  0 0 | 1 * * * * *
trunc( x.o3o.o3o.o&#x ) & ♦ 12  0 4 4 |  6  0 4 12  0  0 12  6  0  0 | 4  0  6  0 4  0 0  0 12 4  0  0  0 | 1 0 0 4  0 0 4 1  0 0 0  0 0 | * 2 * * * *
trunc( xoo3ooo ...&#x ) & ♦  6  6 4 4 |  3  3 4  3  6  3  6  3  6  3 | 1  3  3  3 0  3 1  0  3 1  6  3  3 | 0 1 0 1  3 0 0 0  3 1 1  0 0 | * * 8 * * *
trunc( xoo ... oxo&#x )   ♦  4  8 4 4 |  2  4 4  0  8  4  4  2  8  4 | 0  4  2  4 0  0 0  4  0 0  8  4  4 | 0 0 1 0  4 0 0 0  0 0 0  4 1 | * * * 6 * *
verfA( xoo3ooo3oxo&#x )   ♦  3  3 1 0 |  0  0 0  3  6  3  3  0  3  0 | 0  0  0  0 1  3 1  3  3 0  6  3  0 | 0 0 0 0  0 1 1 0  3 1 0  3 0 | * * * * 8 *
verfB( xoo3ooo3oxo&#x )   ♦  0  0 0 8 |  0  0 0  0  0  0  0 12  0 12 | 0  0  0  0 0  0 0  0  0 8  0  0 24 | 0 0 0 0  0 0 0 2  0 0 8  0 6 | * * * * * 1

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