2rox+sophi

Acronym	...
Name	2rox+sophi (?)
Circumradius	sqrt[5+2 sqrt(5)] = 3.077684
General of army	rox
Colonel of regiment	rox
Confer	non-Grünbaumian masters: rox sophi Grünbaumian relatives: rox+720pip 2rox 2rox+1440{5}+2400{3} general polytopal classes: Wythoffian polychora

Looks like a compound of 2 rox plus sophi, but the vertices coincide by ten, edges coincide by four, while {3}, oct, and ike coincide by pairs.

Incidence matrix according to Dynkin symbol

x3/2x3/2x5o

.   .   . . | 7200 |    1    1    2 |    1    2    2    1 |   2   1   1
------------+------+----------------+---------------------+------------
x   .   . . |    2 | 3600    *    * |    1    2    0    0 |   2   1   0
.   x   . . |    2 |    * 3600    * |    1    0    2    0 |   2   0   1
.   .   x . |    2 |    *    * 7200 |    0    1    1    1 |   1   1   1
------------+------+----------------+---------------------+------------
x3/2x   . . |    6 |    3    3    0 | 1200    *    *    * |   2   0   0
x   .   x . |    4 |    2    0    2 |    * 3600    *    * |   1   1   0
.   x3/2x . |    6 |    0    3    3 |    *    * 2400    * |   1   0   1
.   .   x5o |    5 |    0    0    5 |    *    *    * 1440 |   0   1   1
------------+------+----------------+---------------------+------------
x3/2x3/2x . ♦   24 |   12   12   12 |    4    6    4    0 | 600   *   *
x   .   x5o ♦   10 |    5    0   10 |    0    5    0    2 |   * 720   *
.   x3/2x5o ♦   60 |    0   30   60 |    0    0   20   12 |   *   * 120

x3/2x3/2x5/4o

.   .   .   . | 7200 |    1    1    2 |    1    2    2    1 |   2   1   1
--------------+------+----------------+---------------------+------------
x   .   .   . |    2 | 3600    *    * |    1    2    0    0 |   2   1   0
.   x   .   . |    2 |    * 3600    * |    1    0    2    0 |   2   0   1
.   .   x   . |    2 |    *    * 7200 |    0    1    1    1 |   1   1   1
--------------+------+----------------+---------------------+------------
x3/2x   .   . |    6 |    3    3    0 | 1200    *    *    * |   2   0   0
x   .   x   . |    4 |    2    0    2 |    * 3600    *    * |   1   1   0
.   x3/2x   . |    6 |    0    3    3 |    *    * 2400    * |   1   0   1
.   .   x5/4o |    5 |    0    0    5 |    *    *    * 1440 |   0   1   1
--------------+------+----------------+---------------------+------------
x3/2x3/2x   . ♦   24 |   12   12   12 |    4    6    4    0 | 600   *   *
x   .   x5/4o ♦   10 |    5    0   10 |    0    5    0    2 |   * 720   *
.   x3/2x5/4o ♦   60 |    0   30   60 |    0    0   20   12 |   *   * 120

x3(-x)3x5o

.   .  . . | 7200 |    1    1    2 |    1    2    2    1 |   2   1   1
-----------+------+----------------+---------------------+------------
x   .  . . |    2 | 3600    *    * |    1    2    0    0 |   2   1   0
.  -x  . . |    2 |    * 3600    * |    1    0    2    0 |   2   0   1
.   .  x . |    2 |    *    * 7200 |    0    1    1    1 |   1   1   1
-----------+------+----------------+---------------------+------------
x3(-x) . . |    6 |    3    3    0 | 1200    *    *    * |   2   0   0
x   .  x . |    4 |    2    0    2 |    * 3600    *    * |   1   1   0
. (-x)3x . |    6 |    0    3    3 |    *    * 2400    * |   1   0   1
.   .  x5o |    5 |    0    0    5 |    *    *    * 1440 |   0   1   1
-----------+------+----------------+---------------------+------------
x3(-x)3x . ♦   24 |   12   12   12 |    4    6    4    0 | 600   *   *
x   .  x5o ♦   10 |    5    0   10 |    0    5    0    2 |   * 720   *
. (-x)3x5o ♦   60 |    0   30   60 |    0    0   20   12 |   *   * 120

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