t    
         
         
t       t
         

         
T       T
         
         
    T    

where:
t = x3o3o (tet)
T = o3o3x (dual tet)

Incidence matrix according to Dynkin symbol

xo3ox xo3oo3ox&#x   → height = 1/sqrt(6) = 0.408248
(tratet || bidual tratet)

o.3o. o.3o.3o.    & | 24 |  2  3  6 | 1  6  3  9  18 |  3  6 1  3 15 12  8  6 | 3 2  9  7  9  5 2 | 1 4 3 3
--------------------+----+----------+----------------+------------------------+-------------------+--------
x. .. .. .. ..    & |  2 | 24  *  * | 1  3  0  3   0 |  3  3 0  3  6  3  0  0 | 3 1  9  3  3  1 0 | 1 4 3 1
.. .. x. .. ..    & |  2 |  * 36  * | 0  2  2  0   4 |  1  4 1  0  4  2  4  2 | 2 2  2  4  3  2 2 | 1 2 1 3
oo3oo oo3oo3oo&#x   |  2 |  *  * 72 | 0  0  0  2   4 |  0  0 0  1  4  4  2  2 | 0 0  4  2  4  2 1 | 0 2 2 2
--------------------+----+----------+----------------+------------------------+-------------------+--------
x.3o. .. .. ..    & |  3 |  3  0  0 | 8  *  *  *   * |  3  0 0  3  0  0  0  0 | 3 0  9  0  0  0 0 | 1 4 3 0
x. .. x. .. ..    & |  4 |  2  2  0 | * 36  *  *   * |  1  2 0  0  2  0  0  0 | 2 1  2  2  1  0 0 | 1 2 1 1
.. .. x.3o. ..    & |  3 |  0  3  0 | *  * 24  *   * |  0  2 1  0  0  0  2  0 | 1 2  0  2  0  1 2 | 1 1 0 3
xo .. .. .. ..&#x & |  3 |  1  0  2 | *  *  * 72   * |  0  0 0  1  2  2  0  0 | 0 0  4  1  2  1 0 | 0 2 2 1
.. .. xo .. ..&#x & |  3 |  0  1  2 | *  *  *  * 144 |  0  0 0  0  1  1  1  1 | 0 0  1  1  2  1 1 | 0 1 1 2
--------------------+----+----------+----------------+------------------------+-------------------+--------
x.3o. x. .. ..    & ♦  6 |  6  3  0 | 2  3  0  0   0 | 12  * *  *  *  *  *  * | 2 0  2  0  0  0 0 | 1 2 1 0
x. .. x.3o. ..    & ♦  6 |  3  6  0 | 0  3  2  0   0 |  * 24 *  *  *  *  *  * | 1 1  0  1  0  0 0 | 1 1 0 1
.. .. x.3o.3o.    & ♦  4 |  0  6  0 | 0  0  4  0   0 |  *  * 6  *  *  *  *  * | 0 2  0  0  0  0 2 | 1 0 0 3
xo3ox .. .. ..&#x   ♦  6 |  6  0  6 | 2  0  0  6   0 |  *  * * 12  *  *  *  * | 0 0  4  0  0  0 0 | 0 2 2 0
xo .. xo .. ..&#x & ♦  5 |  2  2  4 | 0  1  0  2   2 |  *  * *  * 72  *  *  * | 0 0  1  1  1  0 0 | 0 1 1 1
xo .. .. .. ox&#x & ♦  4 |  1  1  4 | 0  0  0  2   2 |  *  * *  *  * 72  *  * | 0 0  1  0  1  1 0 | 0 1 1 1
.. .. xo3oo ..&#x & ♦  4 |  0  3  3 | 0  0  1  0   3 |  *  * *  *  *  * 48  * | 0 0  0  1  0  1 1 | 0 1 0 2
.. .. xo .. ox&#x   ♦  4 |  0  2  4 | 0  0  0  0   4 |  *  * *  *  *  *  * 36 | 0 0  0  0  2  0 1 | 0 0 1 2
--------------------+----+----------+----------------+------------------------+-------------------+--------
x.3o. x.3o. ..    & ♦  9 |  9  9  0 | 3  9  3  0   0 |  3  3 0  0  0  0  0  0 | 8 *  *  *  *  * * | 1 1 0 0
x. .. x.3o.3o.    & ♦  8 |  4 12  0 | 0  6  8  0   0 |  0  4 2  0  0  0  0  0 | * 6  *  *  *  * * | 1 0 0 1
xo3ox xo .. ..&#x & ♦  9 |  9  3 12 | 3  3  0 12   6 |  1  0 0  2  3  3  0  0 | * * 24  *  *  * * | 0 1 1 0
xo .. xo3oo ..&#x & ♦  7 |  3  6  6 | 0  3  2  3   6 |  0  1 0  0  3  0  2  0 | * *  * 24  *  * * | 0 1 0 1
xo .. xo .. ox&#x & ♦  6 |  2  3  8 | 0  1  0  4   8 |  0  0 0  0  2  2  0  2 | * *  *  * 36  * * | 0 0 1 1
xo .. .. oo3ox&#x & ♦  5 |  1  3  6 | 0  0  1  3   6 |  0  0 0  0  0  3  2  0 | * *  *  *  * 24 * | 0 1 0 1
.. .. xo3oo3ox&#x   ♦  8 |  0 12 12 | 0  0  8  0  24 |  0  0 2  0  0  0  8  6 | * *  *  *  *  * 6 | 0 0 0 2
--------------------+----+----------+----------------+------------------------+-------------------+--------
x.3o. x.3o.3o.    & ♦ 12 | 12 18  0 | 4 18 12  0   0 |  6 12 3  0  0  0  0  0 | 4 3  0  0  0  0 0 | 2 * * *
xo3ox xo3oo ..&#x & ♦ 12 | 12  9 18 | 4  9  3 18  18 |  3  3 0  3  9  9  6  0 | 1 0  3  3  0  3 0 | * 8 * *
xo3ox xo .. ox&#x   ♦ 12 | 12  6 24 | 4  6  0 24  24 |  2  0 0  4 12 12  0  6 | 0 0  4  0  6  0 0 | * * 6 *
xo .. xo3oo3ox&#x & ♦ 12 |  4 18 24 | 0  6 12 12  48 |  0  4 3  0 12 12 16 12 | 0 1  0  4  6  4 2 | * * * 6

oxox xxoo3oooo3ooxx&#xr   → height(1,2) = height(3,4) = sqrt(3)/2 = 0.866025
                            height(1,4) = height(2,3) = 1/2
                            height(2,4) = 1/sqrt(2) = 0.707107
(cycle of tet, tepe, dual tet, inv. tepe)

o... o...3o...3o...     & | 8  * |  3  2  6 0  0  0 | 3 1  6  6  3 12  6  0  0  0 | 1  3  6  3 12  6  6  3  6  6  2 0 0  0  0 | 3 2  9  6  6  2 3  3 1 2 0 0 | 1 4 3 2 1
.o.. .o..3.o..3.o..     & | * 16 |  0  1  3 1  3  3 | 0 1  3  6  3  3  6  3  3  9 | 0  3  3  3  9  9  3  6  1  3  3 3 1  4  3 | 3 1  9  4  6  4 1  3 3 1 1 1 | 1 4 3 2 1
--------------------------+------+------------------+-----------------------------+-------------------------------------------+------------------------------+----------
.... x... .... ....     & | 2  0 | 12  *  * *  *  * | 2 0  2  0  0  4  0  0  0  0 | 1  1  4  0  4  0  2  0  4  2  0 0 0  0  0 | 2 2  2  4  2  0 2  1 0 2 0 0 | 1 2 1 2 1
oo.. oo..3oo..3oo..&#x  & | 1  1 |  * 16  * *  *  * | 0 1  3  3  0  0  0  0  0  0 | 0  3  3  3  6  3  0  0  0  0  0 0 0  0  0 | 3 1  9  3  3  1 0  0 0 0 0 0 | 1 4 3 1 0
o..o o..o3o..o3o..o&#x  & | 1  1 |  *  * 48 *  *  * | 0 0  0  1  1  2  2  0  0  0 | 0  0  0  1  2  2  2  2  1  2  1 0 0  0  0 | 0 0  4  1  2  1 1  2 1 1 0 0 | 0 2 2 1 1
.x.. .... .... ....     & | 0  2 |  *  *  * 8  *  * | 0 1  0  0  3  0  0  3  0  0 | 0  3  0  3  0  0  3  6  0  0  0 3 0  0  0 | 3 0  9  0  0  0 1  3 3 0 1 0 | 1 4 3 0 1
.... .x.. .... ....     & | 0  2 |  *  *  * * 24  * | 0 0  1  0  0  0  2  1  2  2 | 0  1  2  0  2  2  0  2  0  1  2 2 1  2  1 | 2 1  2  2  2  2 0  1 2 1 1 1 | 1 2 1 2 1
.o.o .o.o3.o.o3.o.o&#x    | 0  2 |  *  *  * *  * 24 | 0 0  0  2  0  0  0  0  0  4 | 0  0  0  1  4  4  0  0  0  0  0 0 0  2  2 | 0 0  4  2  4  2 0  0 0 0 0 1 | 0 2 2 2 0
--------------------------+------+------------------+-----------------------------+-------------------------------------------+------------------------------+----------
.... x...3o... ....     & | 3  0 |  3  0  0 0  0  0 | 8 *  *  *  *  *  *  *  *  * | 1  0  2  0  0  0  0  0  2  0  0 0 0  0  0 | 1 2  0  2  0  0 1  0 0 2 0 0 | 1 1 0 2 1
ox.. .... .... ....&#x  & | 1  2 |  0  2  0 1  0  0 | * 8  *  *  *  *  *  *  *  * | 0  3  0  3  0  0  0  0  0  0  0 0 0  0  0 | 3 0  9  0  0  0 0  0 0 0 0 0 | 1 4 3 0 0
.... xx.. .... ....&#x  & | 2  2 |  1  2  0 0  1  0 | * * 24  *  *  *  *  *  *  * | 0  1  2  0  2  0  0  0  0  0  0 0 0  0  0 | 2 1  2  2  1  0 0  0 0 0 0 0 | 1 2 1 1 0
oo.o oo.o3oo.o3oo.o&#x  & | 1  2 |  0  1  1 0  0  1 | * *  * 48  *  *  *  *  *  * | 0  0  0  1  2  2  0  0  0  0  0 0 0  0  0 | 0 0  4  1  2  1 0  0 0 0 0 0 | 0 2 2 1 0
o..x .... .... ....&#x  & | 1  2 |  0  0  2 1  0  0 | * *  *  * 24  *  *  *  *  * | 0  0  0  1  0  0  2  2  0  0  0 0 0  0  0 | 0 0  4  0  0  0 1  2 1 0 0 0 | 0 2 2 0 1
.... x..o .... ....&#x  & | 2  1 |  1  0  2 0  0  0 | * *  *  *  * 48  *  *  *  * | 0  0  0  0  1  0  1  0  1  1  0 0 0  0  0 | 0 0  1  1  1  0 1  1 0 1 0 0 | 0 1 1 1 1
.... .... .... o..x&#x  & | 1  2 |  0  0  2 0  1  0 | * *  *  *  *  * 48  *  *  * | 0  0  0  0  0  1  0  1  0  1  1 0 0  0  0 | 0 0  1  0  1  1 0  1 1 1 0 0 | 0 1 1 1 1
.x.. .x.. .... ....     & | 0  4 |  0  0  0 2  2  0 | * *  *  *  *  *  * 12  *  * | 0  1  0  0  0  0  0  2  0  0  0 2 0  0  0 | 2 0  2  0  0  0 0  1 2 0 1 0 | 1 2 1 0 1
.... .x..3.o.. ....     & | 0  3 |  0  0  0 0  3  0 | * *  *  *  *  *  *  * 16  * | 0  0  1  0  0  0  0  0  0  0  1 1 1  1  0 | 1 1  0  1  0  1 0  0 1 1 1 1 | 1 1 0 2 1
.... .x.o .... ....&#x    | 0  3 |  0  0  0 0  1  2 | * *  *  *  *  *  *  *  * 48 | 0  0  0  0  1  1  0  0  0  0  0 0 0  1  1 | 0 0  1  1  2  1 0  0 0 0 0 1 | 0 1 1 2 0
--------------------------+------+------------------+-----------------------------+-------------------------------------------+------------------------------+----------
.... x...3o...3o...     & ♦ 4  0 |  6  0  0 0  0  0 | 4 0  0  0  0  0  0  0  0  0 | 2  *  *  *  *  *  *  *  *  *  * * *  *  * | 0 2  0  0  0  0 0  0 0 2 0 0 | 1 0 0 2 1
ox.. xx.. .... ....&#x  & ♦ 2  4 |  1  4  0 2  2  0 | 0 2  2  0  0  0  0  1  0  0 | * 12  *  *  *  *  *  *  *  *  * * *  *  * | 2 0  2  0  0  0 0  0 0 0 0 0 | 1 2 1 0 0
.... xx..3oo.. ....&#x  & ♦ 3  3 |  3  3  0 0  3  0 | 1 0  3  0  0  0  0  0  1  0 | *  * 16  *  *  *  *  *  *  *  * * *  *  * | 1 1  0  1  0  0 0  0 0 0 0 0 | 1 1 0 1 0
oxox .... .... ....&#xr   ♦ 2  4 |  0  4  4 2  0  2 | 0 2  0  4  2  0  0  0  0  0 | *  *  * 12  *  *  *  *  *  *  * * *  *  * | 0 0  4  0  0  0 0  0 0 0 0 0 | 0 2 2 0 0
.... xx.o .... ....&#x  & ♦ 2  3 |  1  2  2 0  1  2 | 0 0  1  2  0  1  0  0  0  1 | *  *  *  * 48  *  *  *  *  *  * * *  *  * | 0 0  1  1  1  0 0  0 0 0 0 0 | 0 1 1 1 0
.... .... .... oo.x&#x  & ♦ 1  3 |  0  1  2 0  1  2 | 0 0  0  2  0  0  1  0  0  1 | *  *  *  *  * 48  *  *  *  *  * * *  *  * | 0 0  1  0  1  1 0  0 0 0 0 0 | 0 1 1 1 0
o..x x..o .... ....&#x  & ♦ 2  2 |  1  0  4 1  0  0 | 0 0  0  0  2  2  0  0  0  0 | *  *  *  *  *  * 24  *  *  *  * * *  *  * | 0 0  1  0  0  0 1  1 0 0 0 0 | 0 1 1 0 1
o..x .... .... o..x&#x  & ♦ 1  4 |  0  0  4 2  2  0 | 0 0  0  0  2  0  2  1  0  0 | *  *  *  *  *  *  * 24  *  *  * * *  *  * | 0 0  1  0  0  0 0  1 1 0 0 0 | 0 1 1 0 1
.... x..o3o..o ....&#x  & ♦ 3  1 |  3  0  3 0  0  0 | 1 0  0  0  0  3  0  0  0  0 | *  *  *  *  *  *  *  * 16  *  * * *  *  * | 0 0  0  1  0  0 1  0 0 1 0 0 | 0 1 0 1 1
.... x..o .... o..x&#x  & ♦ 2  2 |  1  0  4 0  1  0 | 0 0  0  0  0  2  2  0  0  0 | *  *  *  *  *  *  *  *  * 24  * * *  *  * | 0 0  0  0  1  0 0  1 0 1 0 0 | 0 0 1 1 1
.... .... o..o3o..x&#x  & ♦ 1  3 |  0  0  3 0  3  0 | 0 0  0  0  0  0  3  0  1  0 | *  *  *  *  *  *  *  *  *  * 16 * *  *  * | 0 0  0  0  0  1 0  0 1 1 0 0 | 0 1 0 1 1
.x.. .x..3.o.. ....     & ♦ 0  6 |  0  0  0 3  6  0 | 0 0  0  0  0  0  0  3  2  0 | *  *  *  *  *  *  *  *  *  *  * 8 *  *  * | 1 0  0  0  0  0 0  0 1 0 1 0 | 1 1 0 0 1
.... .x..3.o..3.o..     & ♦ 0  4 |  0  0  0 0  6  0 | 0 0  0  0  0  0  0  0  4  0 | *  *  *  *  *  *  *  *  *  *  * * 4  *  * | 0 1  0  0  0  0 0  0 0 1 1 1 | 1 0 0 2 1
.... .x.o3.o.o ....&#x  & ♦ 0  4 |  0  0  0 0  3  3 | 0 0  0  0  0  0  0  0  1  3 | *  *  *  *  *  *  *  *  *  *  * * * 16  * | 0 0  0  1  0  1 0  0 0 0 0 1 | 0 1 0 2 0
.... .x.o .... .o.x&#x    ♦ 0  4 |  0  0  0 0  2  4 | 0 0  0  0  0  0  0  0  0  4 | *  *  *  *  *  *  *  *  *  *  * * *  * 12 | 0 0  0  0  2  0 0  0 0 0 0 1 | 0 0 1 2 0
--------------------------+------+------------------+-----------------------------+-------------------------------------------+------------------------------+----------
ox.. xx..3oo.. ....&#x  & ♦ 3  6 |  3  6  0 3  6  0 | 1 3  6  0  0  0  0  3  2  0 | 0  3  2  0  0  0  0  0  0  0  0 1 0  0  0 | 8 *  *  *  *  * *  * * * * * | 1 1 0 0 0
.... xx..3oo..3oo..&#x  & ♦ 4  4 |  6  4  0 0  6  0 | 4 0  6  0  0  0  0  0  4  0 | 1  0  4  0  0  0  0  0  0  0  0 0 1  0  0 | * 4  *  *  *  * *  * * * * * | 1 0 0 1 0
oxox xxoo .... ....&#xr & ♦ 3  6 |  1  6  8 3  2  4 | 0 3  2  8  4  2  2  1  0  2 | 0  1  0  2  2  2  1  1  0  0  0 0 0  0  0 | * * 24  *  *  * *  * * * * * | 0 1 1 0 0
.... xx.o3oo.o ....&#x  & ♦ 3  4 |  3  3  3 0  3  3 | 1 0  3  3  0  3  0  0  1  3 | 0  0  1  0  3  0  0  0  1  0  0 0 0  1  0 | * *  * 16  *  * *  * * * * * | 0 1 0 1 0
.... xx.o .... oo.x&#x  & ♦ 2  4 |  1  2  4 0  2  4 | 0 0  1  4  0  2  2  0  0  4 | 0  0  0  0  2  2  0  0  0  1  0 0 0  0  1 | * *  *  * 24  * *  * * * * * | 0 0 1 1 0
.... .... oo.o3oo.x&#x  & ♦ 1  4 |  0  1  3 0  3  3 | 0 0  0  3  0  0  3  0  1  3 | 0  0  0  0  0  3  0  0  0  0  1 0 0  1  0 | * *  *  *  * 16 *  * * * * * | 0 1 0 1 0
o..x x..o3o..o ....&#x  & ♦ 3  2 |  3  0  6 1  0  0 | 1 0  0  0  3  6  0  0  0  0 | 0  0  0  0  0  0  3  0  2  0  0 0 0  0  0 | * *  *  *  *  * 8  * * * * * | 0 1 0 0 1
o..x x..o .... o..x&#x  & ♦ 2  4 |  1  0  8 2  2  0 | 0 0  0  0  4  4  4  1  0  0 | 0  0  0  0  0  0  2  2  0  2  0 0 0  0  0 | * *  *  *  *  * * 12 * * * * | 0 0 1 0 1
o..x .... o..o3o..x&#x  & ♦ 1  6 |  0  0  6 3  6  0 | 0 0  0  0  3  0  6  3  2  0 | 0  0  0  0  0  0  0  3  0  0  2 1 0  0  0 | * *  *  *  *  * *  * 8 * * * | 0 1 0 0 1
.... x..o3o..o3o..x&#x  & ♦ 4  4 |  6  0 12 0  6  0 | 4 0  0  0  0 12 12  0  4  0 | 1  0  0  0  0  0  0  0  4  6  4 0 1  0  0 | * *  *  *  *  * *  * * 4 * * | 0 0 0 1 1
.x.. .x..3.o..3.o..     & ♦ 0  8 |  0  0  0 4 12  0 | 0 0  0  0  0  0  0  6  8  0 | 0  0  0  0  0  0  0  0  0  0  0 4 2  0  0 | * *  *  *  *  * *  * * * 2 * | 1 0 0 0 1
.... .x.o3.o.o3.o.x&#x    ♦ 0  8 |  0  0  0 0 12 12 | 0 0  0  0  0  0  0  0  8 24 | 0  0  0  0  0  0  0  0  0  0  0 0 2  8  6 | * *  *  *  *  * *  * * * * 2 | 0 0 0 2 0
--------------------------+------+------------------+-----------------------------+-------------------------------------------+------------------------------+----------
ox.. xx..3oo..3oo..&#x  & ♦ 4  8 |  6  8  0 4 12  0 | 4 4 12  0  0  0  0  6  8  0 | 1  6  8  0  0  0  0  0  0  0  0 4 2  0  0 | 4 2  0  0  0  0 0  0 0 0 1 0 | 2 * * * *
oxox xxoo3oooo ....&#xr & ♦ 4  8 |  3  8 12 4  6  6 | 1 4  6 12  6  6  6  3  2  6 | 0  3  2  3  6  6  3  3  2  0  2 1 0  2  0 | 1 0  3  2  0  2 1  0 1 0 0 0 | * 8 * * *
oxox xxoo .... ooxx&#xr   ♦ 4  8 |  2  8 16 4  4  8 | 0 4  4 16  8  8  8  2  0  8 | 0  2  0  4  8  8  4  4  0  4  0 0 0  0  2 | 0 0  4  0  4  0 0  2 0 0 0 0 | * * 6 * *
.... xx.o3oo.o3oo.x&#x  & ♦ 4  8 |  6  4 12 0 12 12 | 4 0  6 12  0 12 12  0  8 24 | 1  0  4  0 12 12  0  0  4  6  4 0 2  8  6 | 0 1  0  4  6  4 0  0 0 1 0 1 | * * * 4 *
o..x x..o3o..o3o..x&#x  & ♦ 4  8 |  6  0 24 4 12  0 | 4 0  0  0 12 24 24  6  8  0 | 1  0  0  0  0  0 12 12  8 12  8 4 2  0  0 | 0 0  0  0  0  0 4  6 4 2 1 0 | * * * * 2