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The 3 medial vertex layers F3o3x, x3x3f, and o3F3o, together with connecting edges and faces, form a skew dissectioning surface. (That one is shown in the above pictures at outline of the near resp. far half.) It is interesting, that still there beyond 2 completely different continuations are known as well, one which uses in that half thawro cells too, but then in opposite orientation: oxFxofx3xooxFxo3ofxfooo&#xt, and one that gets rid of those fully: oxFxofo3xooxFxx3ofxfoox&#xt.

Also the nearer half can be replaced, then reversing the orientation of the teddies. Together with the second half from here becoming then: oxFxoo3xfoxFx3ooxfox&#xt.

Incidence matrix according to Dynkin symbol

oxFxoo3xooxFx3ofxfox&#xt   → height(1,2) = height(4,5) = sqrt[3-sqrt(5)]/4 = 0.218508
(F=ff=x+f)                   height(2,3) = height(3,4) = height(5,6) = 1/sqrt(8) = 0.353553
(oct || pseudo (x,f)-co || pseudo (F,x)-co || pseudo (x,x,f)-toe || pseudo F-oct || tut)

o.....3o.....3o.....     | 6  *  *  * *  * |  4  4  0  0  0  0  0  0  0  0  0  0  0 0 | 2 2  2  4  2 0  0  0  0 0  0  0 0  0  0  0  0 0 0 0 | 1 2 1 2 0  0 0  0 0 0
.o....3.o....3.o....     | * 12  *  * *  * |  0  2  2  1  2  0  0  0  0  0  0  0  0 0 | 0 0  2  1  2 1  2  1  2 0  0  0 0  0  0  0  0 0 0 0 | 0 1 2 1 1  1 0  0 0 0
..o...3..o...3..o...     | *  * 12  * *  * |  0  0  0  1  0  2  2  0  0  0  0  0  0 0 | 0 0  0  0  2 0  0  0  2 1  1  2 0  0  0  0  0 0 0 0 | 0 0 2 1 0  1 1  0 0 0
...o..3...o..3...o..     | *  *  * 24 *  * |  0  0  0  0  1  0  1  1  1  1  1  0  0 0 | 0 0  0  0  0 0  1  1  1 0  1  1 1  1  1  1  1 0 0 0 | 0 0 1 0 1  1 1  1 1 0
....o.3....o.3....o.     | *  *  *  * 6  * |  0  0  0  0  0  0  0  0  0  4  0  2  0 0 | 0 0  0  0  0 0  0  0  0 0  0  2 0  2  0  0  4 1 0 0 | 0 0 1 0 0  0 2  2 0 0
.....o3.....o3.....o     | *  *  *  * * 12 |  0  0  0  0  0  0  0  0  0  0  2  1  2 1 | 0 0  0  0  0 0  0  0  0 0  0  0 0  0  1  2  2 1 1 2 | 0 0 0 0 0  0 2  1 1 1
-------------------------+-----------------+------------------------------------------+-----------------------------------------------------+----------------------
...... x..... ......     | 2  0  0  0 0  0 | 12  *  *  *  *  *  *  *  *  *  *  *  * * | 1 1  0  1  0 0  0  0  0 0  0  0 0  0  0  0  0 0 0 0 | 1 1 0 1 0  0 0  0 0 0
oo....3oo....3oo....&#x  | 1  1  0  0 0  0 |  * 24  *  *  *  *  *  *  *  *  *  *  * * | 0 0  1  1  1 0  0  0  0 0  0  0 0  0  0  0  0 0 0 0 | 0 1 1 1 0  0 0  0 0 0
.x.... ...... ......     | 0  2  0  0 0  0 |  *  * 12  *  *  *  *  *  *  *  *  *  * * | 0 0  1  0  0 1  1  0  0 0  0  0 0  0  0  0  0 0 0 0 | 0 1 1 0 1  0 0  0 0 0
.oo...3.oo...3.oo...&#x  | 0  1  1  0 0  0 |  *  *  * 12  *  *  *  *  *  *  *  *  * * | 0 0  0  0  2 0  0  0  2 0  0  0 0  0  0  0  0 0 0 0 | 0 0 2 1 0  1 0  0 0 0
.o.o..3.o.o..3.o.o..&#x  | 0  1  0  1 0  0 |  *  *  *  * 24  *  *  *  *  *  *  *  * * | 0 0  0  0  0 0  1  1  1 0  0  0 0  0  0  0  0 0 0 0 | 0 0 1 0 1  1 0  0 0 0
...... ...... ..x...     | 0  0  2  0 0  0 |  *  *  *  *  * 12  *  *  *  *  *  *  * * | 0 0  0  0  1 0  0  0  0 1  0  1 0  0  0  0  0 0 0 0 | 0 0 1 1 0  0 1  0 0 0
..oo..3..oo..3..oo..&#x  | 0  0  1  1 0  0 |  *  *  *  *  *  * 24  *  *  *  *  *  * * | 0 0  0  0  0 0  0  0  1 0  1  1 0  0  0  0  0 0 0 0 | 0 0 1 0 0  1 1  0 0 0
...x.. ...... ......     | 0  0  0  2 0  0 |  *  *  *  *  *  *  * 12  *  *  *  *  * * | 0 0  0  0  0 0  1  0  0 0  0  0 1  1  1  0  0 0 0 0 | 0 0 1 0 1  0 0  1 1 0
...... ...x.. ......     | 0  0  0  2 0  0 |  *  *  *  *  *  *  *  * 12  *  *  *  * * | 0 0  0  0  0 0  0  1  0 0  1  0 1  0  0  1  0 0 0 0 | 0 0 0 0 1  1 1  0 1 0
...oo.3...oo.3...oo.&#x  | 0  0  0  1 1  0 |  *  *  *  *  *  *  *  *  * 24  *  *  * * | 0 0  0  0  0 0  0  0  0 0  0  1 0  1  0  0  1 0 0 0 | 0 0 1 0 0  0 1  1 0 0
...o.o3...o.o3...o.o&#x  | 0  0  0  1 0  1 |  *  *  *  *  *  *  *  *  *  * 24  *  * * | 0 0  0  0  0 0  0  0  0 0  0  0 0  0  1  1  1 0 0 0 | 0 0 0 0 0  0 1  1 1 0
....oo3....oo3....oo&#x  | 0  0  0  0 1  1 |  *  *  *  *  *  *  *  *  *  *  * 12  * * | 0 0  0  0  0 0  0  0  0 0  0  0 0  0  0  0  2 1 0 0 | 0 0 0 0 0  0 2  1 0 0
...... .....x ......     | 0  0  0  0 0  2 |  *  *  *  *  *  *  *  *  *  *  *  * 12 * | 0 0  0  0  0 0  0  0  0 0  0  0 0  0  0  1  0 0 1 1 | 0 0 0 0 0  0 1  0 1 1
...... ...... .....x     | 0  0  0  0 0  2 |  *  *  *  *  *  *  *  *  *  *  *  *  * 6 | 0 0  0  0  0 0  0  0  0 0  0  0 0  0  0  0  0 1 0 2 | 0 0 0 0 0  0 2  0 0 1
-------------------------+-----------------+------------------------------------------+-----------------------------------------------------+----------------------
o.....3x..... ......     | 3  0  0  0 0  0 |  3  0  0  0  0  0  0  0  0  0  0  0  0 0 | 4 *  *  *  * *  *  *  * *  *  * *  *  *  *  * * * * | 1 1 0 0 0  0 0  0 0 0
...... x.....3o.....     | 3  0  0  0 0  0 |  3  0  0  0  0  0  0  0  0  0  0  0  0 0 | * 4  *  *  * *  *  *  * *  *  * *  *  *  *  * * * * | 1 0 0 1 0  0 0  0 0 0
ox.... ...... ......&#x  | 1  2  0  0 0  0 |  0  2  1  0  0  0  0  0  0  0  0  0  0 0 | * * 12  *  * *  *  *  * *  *  * *  *  *  *  * * * * | 0 1 1 0 0  0 0  0 0 0
...... xo.... ......&#x  | 2  1  0  0 0  0 |  1  2  0  0  0  0  0  0  0  0  0  0  0 0 | * *  * 12  * *  *  *  * *  *  * *  *  *  *  * * * * | 0 1 0 1 0  0 0  0 0 0
...... ...... ofx...&#xt | 1  2  2  0 0  0 |  0  2  0  2  0  1  0  0  0  0  0  0  0 0 | * *  *  * 12 *  *  *  * *  *  * *  *  *  *  * * * * | 0 0 1 1 0  0 0  0 0 0
.x....3.o.... ......     | 0  3  0  0 0  0 |  0  0  3  0  0  0  0  0  0  0  0  0  0 0 | * *  *  *  * 4  *  *  * *  *  * *  *  *  *  * * * * | 0 1 0 0 1  0 0  0 0 0
.x.x.. ...... ......&#x  | 0  2  0  2 0  0 |  0  0  1  0  2  0  0  1  0  0  0  0  0 0 | * *  *  *  * * 12  *  * *  *  * *  *  *  *  * * * * | 0 0 1 0 1  0 0  0 0 0
...... .o.x.. ......&#x  | 0  1  0  2 0  0 |  0  0  0  0  2  0  0  0  1  0  0  0  0 0 | * *  *  *  * *  * 12  * *  *  * *  *  *  *  * * * * | 0 0 0 0 1  1 0  0 0 0
.ooo..3.ooo..3.ooo..&#x  | 0  1  1  1 0  0 |  0  0  0  1  1  0  1  0  0  0  0  0  0 0 | * *  *  *  * *  *  * 24 *  *  * *  *  *  *  * * * * | 0 0 1 0 0  1 0  0 0 0
...... ..o...3..x...     | 0  0  3  0 0  0 |  0  0  0  0  0  3  0  0  0  0  0  0  0 0 | * *  *  *  * *  *  *  * 4  *  * *  *  *  *  * * * * | 0 0 0 1 0  0 1  0 0 0
...... ..ox.. ......&#x  | 0  0  1  2 0  0 |  0  0  0  0  0  0  2  0  1  0  0  0  0 0 | * *  *  *  * *  *  *  * * 12  * *  *  *  *  * * * * | 0 0 0 0 0  1 1  0 0 0
...... ...... ..xfo.&#xt | 0  0  2  2 1  0 |  0  0  0  0  0  1  2  0  0  2  0  0  0 0 | * *  *  *  * *  *  *  * *  * 12 *  *  *  *  * * * * | 0 0 1 0 0  0 1  0 0 0
...x..3...x.. ......     | 0  0  0  6 0  0 |  0  0  0  0  0  0  0  3  3  0  0  0  0 0 | * *  *  *  * *  *  *  * *  *  * 4  *  *  *  * * * * | 0 0 0 0 1  0 0  0 1 0
...xo. ...... ......&#x  | 0  0  0  2 1  0 |  0  0  0  0  0  0  0  1  0  2  0  0  0 0 | * *  *  *  * *  *  *  * *  *  * * 12  *  *  * * * * | 0 0 1 0 0  0 0  1 0 0
...x.o ...... ......&#x  | 0  0  0  2 0  1 |  0  0  0  0  0  0  0  1  0  0  2  0  0 0 | * *  *  *  * *  *  *  * *  *  * *  * 12  *  * * * * | 0 0 0 0 0  0 0  1 1 0
...... ...x.x ......&#x  | 0  0  0  2 0  2 |  0  0  0  0  0  0  0  0  1  0  2  0  1 0 | * *  *  *  * *  *  *  * *  *  * *  *  * 12  * * * * | 0 0 0 0 0  0 1  0 1 0
...ooo3...ooo3...ooo&#x  | 0  0  0  1 1  1 |  0  0  0  0  0  0  0  0  0  1  1  1  0 0 | * *  *  *  * *  *  *  * *  *  * *  *  *  * 24 * * * | 0 0 0 0 0  0 1  1 0 0
...... ...... ....ox&#x  | 0  0  0  0 1  2 |  0  0  0  0  0  0  0  0  0  0  0  2  0 1 | * *  *  *  * *  *  *  * *  *  * *  *  *  *  * 6 * * | 0 0 0 0 0  0 2  0 0 0
.....o3.....x ......     | 0  0  0  0 0  3 |  0  0  0  0  0  0  0  0  0  0  0  0  3 0 | * *  *  *  * *  *  *  * *  *  * *  *  *  *  * * 4 * | 0 0 0 0 0  0 0  0 1 1
...... .....x3.....x     | 0  0  0  0 0  6 |  0  0  0  0  0  0  0  0  0  0  0  0  3 3 | * *  *  *  * *  *  *  * *  *  * *  *  *  *  * * * 4 | 0 0 0 0 0  0 1  0 0 1
-------------------------+-----------------+------------------------------------------+-----------------------------------------------------+----------------------
o.....3x.....3o.....     ♦ 6  0  0  0 0  0 | 12  0  0  0  0  0  0  0  0  0  0  0  0 0 | 4 4  0  0  0 0  0  0  0 0  0  0 0  0  0  0  0 0 0 0 | 1 * * * *  * *  * * *
ox....3xo.... ......&#x  ♦ 3  3  0  0 0  0 |  3  6  3  0  0  0  0  0  0  0  0  0  0 0 | 1 0  3  3  0 1  0  0  0 0  0  0 0  0  0  0  0 0 0 0 | * 4 * * *  * *  * * *
oxFxo. ...... ofxfo.&#xt ♦ 1  4  4  4 1  0 |  0  4  2  4  4  2  4  2  0  4  0  0  0 0 | 0 0  2  0  2 0  2  0  4 0  0  2 0  2  0  0  0 0 0 0 | * * 6 * *  * *  * * *
...... xoo...3ofx...&#xt ♦ 3  3  3  0 0  0 |  3  6  0  3  0  3  0  0  0  0  0  0  0 0 | 0 1  0  3  3 0  0  0  0 1  0  0 0  0  0  0  0 0 0 0 | * * * 4 *  * *  * * *
.x.x..3.o.x.. ......&#x  ♦ 0  3  0  6 0  0 |  0  0  3  0  6  0  0  3  3  0  0  0  0 0 | 0 0  0  0  0 1  3  3  0 0  0  0 1  0  0  0  0 0 0 0 | * * * * 4  * *  * * *
...... .oox.. ......&#x  ♦ 0  1  1  2 0  0 |  0  0  0  1  2  0  2  0  1  0  0  0  0 0 | 0 0  0  0  0 0  0  1  2 0  1  0 0  0  0  0  0 0 0 0 | * * * * * 12 *  * * *
...... ..oxFx3..xfox&#xt ♦ 0  0  3  6 3  6 |  0  0  0  0  0  3  6  0  3  6  6  6  3 3 | 0 0  0  0  0 0  0  0  0 1  3  3 0  0  0  3  6 3 0 1 | * * * * *  * 4  * * *
...xoo ...... ......&#x  ♦ 0  0  0  2 1  1 |  0  0  0  0  0  0  0  1  0  2  2  1  0 0 | 0 0  0  0  0 0  0  0  0 0  0  0 0  1  1  0  2 0 0 0 | * * * * *  * * 12 * *
...x.o3...x.x ......&#x  ♦ 0  0  0  6 0  3 |  0  0  0  0  0  0  0  3  3  0  6  0  3 0 | 0 0  0  0  0 0  0  0  0 0  0  0 1  0  3  3  0 0 1 0 | * * * * *  * *  * 4 *
.....o3.....x3.....x     ♦ 0  0  0  0 0 12 |  0  0  0  0  0  0  0  0  0  0  0  0 12 6 | 0 0  0  0  0 0  0  0  0 0  0  0 0  0  0  0  0 0 4 4 | * * * * *  * *  * * 1