©

Excavating a dodecahedron by 12 peppies and then Stott expanding that outcome, thereby blowing up every vertex into pentagons, the outer (original) edges into squares, and the triangles into hexagons: this is how this very pleasing tetraform acoptic polyhedron, mentioned in 2022 by T. Dorozinski, could be derived.

This tetraform acoptic polyhedron has the following vertex radii:

R( x3f5x ) = sqrt[47+20 sqrt(5)]/2 = 4.788563
R( f3o5u ) = sqrt[37+14 sqrt(5)]/2 = 4.132340
R( o3o5F ) = sqrt[27+12 sqrt(5)]/2 = 3.668542
R( E3o5x ) = sqrt[27+ 8 sqrt(5)]/2 = 3.349946
where: E = 2f-x = f+v = sqrt(5), F = x+f = ff

Incidence matrix according to Dynkin symbol

xfoE3fooo5xuFx&#zxt   → all existing heights = 0

o...3o...5o...     | 120  *  *  * |  1  1   1  0  0  0 |  1  1  1  0  [4,5a,6]
.o..3.o..5.o..     |   * 60  *  * |  0  0   2  1  1  0 |  0  2  2  0  [5a2,62]
..o.3..o.5..o.     |   *  * 20  * |  0  0   0  3  0  0 |  0  3  0  0  [5a3]
...o3...o5...o     |   *  *  * 60 |  0  0   0  0  1  2 |  0  0  2  1  [5b,62]
-------------------+--------------+--------------------+------------
x... .... ....     |   2  0  0  0 | 60  *   *  *  *  * |  1  1  0  0
.... .... x...     |   2  0  0  0 |  * 60   *  *  *  * |  1  0  1  0
oo..3oo..5oo..&#x  |   1  1  0  0 |  *  * 120  *  *  * |  0  1  1  0
.oo.3.oo.5.oo.&#x  |   0  1  1  0 |  *  *   * 60  *  * |  0  2  0  0
.o.o3.o.o5.o.o&#x  |   0  1  0  1 |  *  *   *  * 60  * |  0  0  2  0
.... .... ...x     |   0  0  0  2 |  *  *   *  *  * 60 |  0  0  1  1
-------------------+--------------+--------------------+------------
x... .... x...     |   4  0  0  0 |  2  2   0  0  0  0 | 30  *  *  *  {4}
xfo. .... ....&#xt |   2  2  1  0 |  1  0   2  2  0  0 |  * 60  *  *  {5a} (light blue)
.... .... xu.x&#xt |   2  2  0  2 |  0  1   2  0  2  1 |  *  * 60  *  {6}
.... ...o5...x     |   0  0  0  5 |  0  0   0  0  0  5 |  *  *  * 12  {5b} (magenta)