Acronym ...
Name magnaursachoron,
cell-expanded tetrahedral ursachoron
 
top-view, centered at co:
 ©
base-view, centered at tut:
 ©
side-view, centered at teddi-column:
 ©
Circumradius ...
General of army (is itself convex)
Colonel of regiment (is itself locally convex)

Incidence matrix according to Dynkin symbol

xxFVF(Vx)fox-3-ofxxf(oF)xxx-3-xoooo(xo)xfo-&#xt   → height(1,2) = height(8,9) = 1/sqrt(8) = 0.353553
                                                    height(2,3) = height(5,67) = heigh(67,8) = sqrt[3+sqrt(5)]/4 = 0.572061
                                                    height(3,4) = height(4,5) = sqrt[7+2 sqrt(5)]/4 = 0.925615
                                                    height(9,10) = sqrt[3-sqrt(5)]/4 = 0.218508

o....(..)...-3-o....(..)...-3-o....(..)...      | 12  *  *  *  *  *  *  *  *  * |  2  2  2 0  0  0  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | 1 2 1  2  2  1 0 0  0 0  0  0  0 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 1 2 1 1 0 0  0 0 0  0 0 0
.o...(..)...-3-.o...(..)...-3-.o...(..)...      |  * 12  *  *  *  *  *  *  *  * |  0  0  2 1  1  0  0  0  0  0  0  0  0 0  0  0  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  0 0  0  0 0 0 | 0 1 2 1 0 0  0 0 0  0 0 0
..o..(..)...-3-..o..(..)...-3-..o..(..)...      |  *  * 12  *  *  *  *  *  *  * |  0  0  0 0  1  2  1  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | 0 0 0  0  0  2 1 1  2 0  0  0  0 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 0 2 1 1 0  0 0 0  0 0 0
...o.(..)...-3-...o.(..)...-3-...o.(..)...      |  *  *  * 12  *  *  *  *  *  * |  0  0  0 0  0  0  1  2  1  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | 0 0 0  0  0  0 1 0  2 1  2  0  0 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 0 2 0 1 1  0 0 0  0 0 0
....o(..)...-3-....o(..)...-3-....o(..)...      |  *  *  *  * 12  *  *  *  *  * |  0  0  0 0  0  0  0  0  1  2  1  0  0 0  0  0  0  0  0  0  0 0  0 | 0 0 0  0  0  0 1 0  0 0  2  1  2 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 0 2 0 0 1  1 0 0  0 0 0
.....(o.)...-3-.....(o.)...-3-.....(o.)...      |  *  *  *  *  * 12  *  *  *  * |  0  0  0 0  0  0  0  0  0  2  0  2  2 0  0  0  0  0  0  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 0  0  0 0 0 | 0 0 1 0 0 1  2 1 0  0 0 0
.....(.o)...-3-.....(.o)...-3-.....(.o)...      |  *  *  *  *  *  * 12  *  *  * |  0  0  0 0  0  0  0  0  0  0  1  0  0 1  2  0  0  0  2  0  0 0  0 | 0 0 0  0  0  0 1 0  0 0  0  0  2 0  0  0  2  1  0  0  0  0 0  0  0 0 0 | 0 0 2 0 0 0  1 0 1  0 0 0
.....(..)o..-3-.....(..)o..-3-.....(..)o..      |  *  *  *  *  *  *  * 24  *  * |  0  0  0 0  0  0  0  0  0  0  0  0  1 0  1  1  1  1  0  0  0 0  0 | 0 0 0  0  0  0 0 0  0 0  0  0  1 0  1  1  1  1  1  1  1  1 0  0  0 0 0 | 0 0 1 0 0 0  1 1 1  2 0 0
.....(..).o.-3-.....(..).o.-3-.....(..).o.      |  *  *  *  *  *  *  *  * 12  * |  0  0  0 0  0  0  0  0  0  0  0  0  0 0  0  0  0  2  2  2  2 0  0 | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  0  1  0  2  0  0  2 1  1  2 0 0 | 0 0 1 0 0 0  0 0 1  1 1 0
.....(..)..o-3-.....(..)..o-3-.....(..)..o      |  *  *  *  *  *  *  *  *  * 12 |  0  0  0 0  0  0  0  0  0  0  0  0  0 0  0  0  0  0  2  0  2 1  2 | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  0  0  0  0  1  2  2 0  2  2 2 1 | 0 0 0 0 0 0  0 1 1  1 2 1
------------------------------------------------+-------------------------------+-------------------------------------------------------------------+------------------------------------------------------------------------+--------------------------
x....(..)...   .....(..)...   .....(..)...      |  2  0  0  0  0  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  0  0 0  0  0 0 0 | 1 1 1 0 0 0  0 0 0  0 0 0
.....(..)...   .....(..)...   x....(..)...      |  2  0  0  0  0  0  0  0  0  0 |  * 12  * *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 1 1  0  1  0 0 0  0 0  0  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 0 0
oo...(..)...-3-oo...(..)...-3-oo...(..)...-&#x  |  1  1  0  0  0  0  0  0  0  0 |  *  * 24 *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  1  1  1 0 0  0 0  0  0  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 0 0
.x...(..)...   .....(..)...   .....(..)...      |  0  2  0  0  0  0  0  0  0  0 |  *  *  * 6  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  2  0  0 1 0  0 0  0  0  0 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 1 2 0 0 0  0 0 0  0 0 0
.oo..(..)...-3-.oo..(..)...-3-.oo..(..)...-&#x  |  0  1  1  0  0  0  0  0  0  0 |  *  *  * * 12  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  2 1 0  0 0  0  0  0 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
.....(..)...   ..x..(..)...   .....(..)...      |  0  0  2  0  0  0  0  0  0  0 |  *  *  * *  * 12  *  *  *  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  1 0 1  1 0  0  0  0 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 0
..oo.(..)...-3-..oo.(..)...-3-..oo.(..)...-&#x  |  0  0  1  1  0  0  0  0  0  0 |  *  *  * *  *  * 12  *  *  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 1 0  2 0  0  0  0 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 0 2 0 1 0  0 0 0  0 0 0
.....(..)...   ...x.(..)...   .....(..)...      |  0  0  0  2  0  0  0  0  0  0 |  *  *  * *  *  *  * 12  *  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 0 0  1 1  1  0  0 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 0 1 0 1 1  0 0 0  0 0 0
...oo(..)...-3-...oo(..)...-3-...oo(..)...-&#x  |  0  0  0  1  1  0  0  0  0  0 |  *  *  * *  *  *  *  * 12  *  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 1 0  0 0  2  0  0 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 0 2 0 0 1  0 0 0  0 0 0
....o(o.)...-3-....o(o.)...-3-....o(o.)...-&#x  |  0  0  0  0  1  1  0  0  0  0 |  *  *  * *  *  *  *  *  * 24  *  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 0 0  0 0  1  1  1 0  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
....o(.o)...-3-....o(.o)...-3-....o(.o)...-&#x  |  0  0  0  0  1  0  1  0  0  0 |  *  *  * *  *  *  *  *  *  * 12  *  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 1 0  0 0  0  0  2 0  0  0  0  0  0  0  0  0 0  0  0 0 0 | 0 0 2 0 0 0  1 0 0  0 0 0
.....(..)...   .....(..)...   .....(x.)...      |  0  0  0  0  0  2  0  0  0  0 |  *  *  * *  *  *  *  *  *  *  * 12  * *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 0 0  0 0  0  1  0 1  0  1  0  0  0  0  0  0 0  0  0 0 0 | 0 0 0 0 0 1  1 1 0  0 0 0
.....(o.)o..-3-.....(o.)o..-3-.....(o.)o..-&#x  |  0  0  0  0  0  1  0  1  0  0 |  *  *  * *  *  *  *  *  *  *  *  * 24 *  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 0 0  0 0  0  0  1 0  1  1  0  0  0  0  0  0 0  0  0 0 0 | 0 0 1 0 0 0  1 1 0  0 0 0
.....(.x)...   .....(..)...   .....(..)...      |  0  0  0  0  0  0  2  0  0  0 |  *  *  * *  *  *  *  *  *  *  *  *  * 6  *  *  *  *  *  *  * *  * | 0 0 0  0  0  0 1 0  0 0  0  0  0 0  0  0  2  0  0  0  0  0 0  0  0 0 0 | 0 0 2 0 0 0  0 0 1  0 0 0
.....(.o)o..-3-.....(.o)o..-3-.....(.o)o..-&#x  |  0  0  0  0  0  0  1  1  0  0 |  *  *  * *  *  *  *  *  *  *  *  *  * * 24  *  *  *  *  *  * *  * | 0 0 0  0  0  0 0 0  0 0  0  0  1 0  0  0  1  1  0  0  0  0 0  0  0 0 0 | 0 0 1 0 0 0  1 0 1  0 0 0
.....(..)...   .....(..)x..   .....(..)...      |  0  0  0  0  0  0  0  2  0  0 |  *  *  * *  *  *  *  *  *  *  *  *  * *  * 12  *  *  *  *  * *  * | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  1  0  0  0  1  0  1  0 0  0  0 0 0 | 0 0 1 0 0 0  0 1 0  1 0 0
.....(..)...   .....(..)...   .....(..)x..      |  0  0  0  0  0  0  0  2  0  0 |  *  *  * *  *  *  *  *  *  *  *  *  * *  *  * 12  *  *  *  * *  * | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  1  0  1  0  1  0  0 0  0  0 0 0 | 0 0 0 0 0 0  1 1 1  0 0 0
.....(..)oo.-3-.....(..)oo.-3-.....(..)oo.-&#x  |  0  0  0  0  0  0  0  1  1  0 |  *  *  * *  *  *  *  *  *  *  *  *  * *  *  *  * 24  *  *  * *  * | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  0  1  0  1  0  0  1 0  0  0 0 0 | 0 0 1 0 0 0  0 0 1  1 0 0
.....(..)o.o-3-.....(..)o.o-3-.....(..)o.o-&#x  |  0  0  0  0  0  0  0  1  0  1 |  *  *  * *  *  *  *  *  *  *  *  *  * *  *  *  *  * 24  *  * *  * | 0 0 0  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 0 0 0 0 0  0 1 1  1 0 0
.....(..)...   .....(..).x.   .....(..)...      |  0  0  0  0  0  0  0  0  2  0 |  *  *  * *  *  *  *  *  *  *  *  *  * *  *  *  *  *  * 12  * *  * | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  0  0  0  1  0  0  0 1  0  1 0 0 | 0 0 1 0 0 0  0 0 0  1 1 0
.....(..).oo-3-.....(..).oo-3-.....(..).oo-&#x  |  0  0  0  0  0  0  0  0  1  1 |  *  *  * *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  * 24 *  * | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  0  0  0  0  0  0  1 0  1  1 0 0 | 0 0 0 0 0 0  0 0 1  1 1 0
.....(..)..x   .....(..)...   .....(..)...      |  0  0  0  0  0  0  0  0  0  2 |  *  *  * *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * 6  * | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  0  0  0  0  0  0  0 0  2  0 2 0 | 0 0 0 0 0 0  0 0 1  0 2 1
.....(..)...   .....(..)..x   .....(..)...      |  0  0  0  0  0  0  0  0  0  2 |  *  *  * *  *  *  *  *  *  *  *  *  * *  *  *  *  *  *  *  * * 12 | 0 0 0  0  0  0 0 0  0 0  0  0  0 0  0  0  0  0  0  1  0  0 0  0  1 1 1 | 0 0 0 0 0 0  0 1 0  1 1 1
------------------------------------------------+-------------------------------+-------------------------------------------------------------------+------------------------------------------------------------------------+--------------------------
x....(..)...-3-o....(..)...   .....(..)...      |  3  0  0  0  0  0  0  0  0  0 |  3  0  0 0  0  0  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | 4 * *  *  *  * * *  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 1 0 1 0 0 0  0 0 0  0 0 0
x....(..)...   .....(..)...   x....(..)...      |  4  0  0  0  0  0  0  0  0  0 |  2  2  0 0  0  0  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * 6 *  *  *  * * *  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 1 1 0 0 0 0  0 0 0  0 0 0
.....(..)...   o....(..)...-3-x....(..)...      |  3  0  0  0  0  0  0  0  0  0 |  0  3  0 0  0  0  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * 4  *  *  * * *  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 1 0 0 1 0 0  0 0 0  0 0 0
xx...(..)...   .....(..)...   .....(..)...-&#x  |  2  2  0  0  0  0  0  0  0  0 |  1  0  2 1  0  0  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * * 12  *  * * *  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 1 1 0 0 0  0 0 0  0 0 0
.....(..)...   .....(..)...   xo...(..)...-&#x  |  2  1  0  0  0  0  0  0  0  0 |  0  1  2 0  0  0  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * *  * 12  * * *  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 1 0 1 0 0  0 0 0  0 0 0
.....(..)...   ofx..(..)...   .....(..)...-&#xt |  1  2  2  0  0  0  0  0  0  0 |  0  0  2 0  2  1  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * *  *  * 12 * *  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 1 1 0 0  0 0 0  0 0 0
.xFVF(.x)...   .....(..)...   .....(..)...-&#xt |  0  2  2  2  2  0  2  0  0  0 |  0  0  0 1  2  0  2  0  2  0  2  0  0 1  0  0  0  0  0  0  0 0  0 | * * *  *  *  * 6 *  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 2 0 0 0  0 0 0  0 0 0
.....(..)...   ..x..(..)...-3-..o..(..)...      |  0  0  3  0  0  0  0  0  0  0 |  0  0  0 0  0  3  0  0  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * *  *  *  * * 4  * *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 0 1 1 0  0 0 0  0 0 0
.....(..)...   ..xx.(..)...   .....(..)...-&#x  |  0  0  2  2  0  0  0  0  0  0 |  0  0  0 0  0  1  2  1  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * *  *  *  * * * 12 *  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 1 0 1 0  0 0 0  0 0 0
.....(..)...   ...x.(..)...-3-...o.(..)...      |  0  0  0  3  0  0  0  0  0  0 |  0  0  0 0  0  0  0  3  0  0  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * *  *  *  * * *  * 4  *  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 0 0 1 1  0 0 0  0 0 0
.....(..)...   ...xf(o.)...   .....(..)...-&#xt |  0  0  0  2  2  1  0  0  0  0 |  0  0  0 0  0  0  0  1  2  2  0  0  0 0  0  0  0  0  0  0  0 0  0 | * * *  *  *  * * *  * * 12  *  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 1 0 0 1  0 0 0  0 0 0
.....(..)...   .....(..)...   ....x(o.)...-&#x  |  0  0  0  0  1  2  0  0  0  0 |  0  0  0 0  0  0  0  0  0  2  0  1  0 0  0  0  0  0  0  0  0 0  0 | * * *  *  *  * * *  * *  * 12  * *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 0 0 0 1  1 0 0  0 0 0
....o(oo)o..-3-....o(oo)o..-3-....o(oo)o..-&#xr |  0  0  0  0  1  1  1  1  0  0 |  0  0  0 0  0  0  0  0  0  1  1  0  1 0  1  0  0  0  0  0  0 0  0 | * * *  *  *  * * *  * *  *  * 24 *  *  *  *  *  *  *  *  * *  *  * * * | 0 0 1 0 0 0  1 0 0  0 0 0
.....(..)...   .....(o.)...-3-.....(x.)...      |  0  0  0  0  0  3  0  0  0  0 |  0  0  0 0  0  0  0  0  0  0  0  3  0 0  0  0  0  0  0  0  0 0  0 | * * *  *  *  * * *  * *  *  *  * 4  *  *  *  *  *  *  *  * *  *  * * * | 0 0 0 0 0 1  0 1 0  0 0 0
.....(..)...   .....(o.)x..   .....(..)...-&#x  |  0  0  0  0  0  1  0  2  0  0 |  0  0  0 0  0  0  0  0  0  0  0  0  2 0  0  1  0  0  0  0  0 0  0 | * * *  *  *  * * *  * *  *  *  * * 12  *  *  *  *  *  *  * *  *  * * * | 0 0 1 0 0 0  0 1 0  0 0 0
.....(..)...   .....(..)...   .....(x.)x..-&#x  |  0  0  0  0  0  2  0  2  0  0 |  0  0  0 0  0  0  0  0  0  0  0  1  2 0  0  0  1  0  0  0  0 0  0 | * * *  *  *  * * *  * *  *  *  * *  * 12  *  *  *  *  *  * *  *  * * * | 0 0 0 0 0 0  1 1 0  0 0 0
.....(.x)fo.   .....(..)...   .....(..)...-&#xt |  0  0  0  0  0  0  2  2  1  0 |  0  0  0 0  0  0  0  0  0  0  0  0  0 1  2  0  0  2  0  0  0 0  0 | * * *  *  *  * * *  * *  *  *  * *  *  * 12  *  *  *  *  * *  *  * * * | 0 0 1 0 0 0  0 0 1  0 0 0
.....(..)...   .....(..)...   .....(.o)x..-&#x  |  0  0  0  0  0  0  1  2  0  0 |  0  0  0 0  0  0  0  0  0  0  0  0  0 0  2  0  1  0  0  0  0 0  0 | * * *  *  *  * * *  * *  *  *  * *  *  *  * 12  *  *  *  * *  *  * * * | 0 0 0 0 0 0  1 0 1  0 0 0
.....(..)...   .....(..)xx.   .....(..)...-&#x  |  0  0  0  0  0  0  0  2  2  0 |  0  0  0 0  0  0  0  0  0  0  0  0  0 0  0  1  0  2  0  1  0 0  0 | * * *  *  *  * * *  * *  *  *  * *  *  *  *  * 12  *  *  * *  *  * * * | 0 0 1 0 0 0  0 0 0  1 0 0
.....(..)...   .....(..)x.x   .....(..)...-&#x  |  0  0  0  0  0  0  0  2  0  2 |  0  0  0 0  0  0  0  0  0  0  0  0  0 0  0  1  0  0  2  0  0 0  1 | * * *  *  *  * * *  * *  *  *  * *  *  *  *  *  * 12  *  * *  *  * * * | 0 0 0 0 0 0  0 1 0  1 0 0
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