Acronym ...
Name three squaf blend,
"thah-squares star" atop cube
Circumradius sqrt[(4+sqrt(2))/7] = 0.879465
Confer "coord-axes edge star" || cube   "coord-planes square star" || cube   "coord-planes squares star" || "coord-planes squares star"  

Incidence matrix according to Dynkin symbol

reduced( xo3/2xo4ox&#x )
("thah-squares star" || cube)

identif.( o.3/2o.4o.      ) | 6 * |  4  4  0 | 2  8  4 0 |  4 4 0
         .o3/2.o4.o         | * 8 |  0  3  3 | 0  3  6 3 |  3 3 1
----------------------------+-----+----------+-----------+-------
identif.( ..   x. ..    & ) | 2 0 | 12  *  * | 1  2  0 0 |  1 2 0
identif.( oo3/2oo4oo&#x   ) | 1 1 |  * 24  * | 0  2  2 0 |  2 2 0
          ..   .. .x        | 0 2 |  *  * 12 | 0  0  2 2 |  1 2 1
----------------------------+-----+----------+-----------+-------
identif.( ..   x.4o.      ) | 4 0 |  4  0  0 | 3  *  * * |  0 2 0
identif.( ..   xo ..&#x & ) | 2 1 |  1  2  0 | * 24  * * |  1 1 0
          ..   .. ox&#x     | 1 2 |  0  2  1 | *  * 24 * |  1 1 0
          ..   .o4.x        | 0 4 |  0  0  4 | *  *  * 6 |  0 1 1
----------------------------+-----+----------+-----------+-------
          xo   .. ox&#x      2 2 |  1  4  1 | 0  2  2 0 | 12 * *
          ..   xo4ox&#x      4 4 |  4  8  4 | 1  4  4 1 |  * 6 *
          .o3/2.o4.x         0 8 |  0  0 12 | 0  0  0 6 |  * * 1

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