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Right by construction this polyhedron is biformic, i.e. the same as uniform, just using 2 vertex types.

This external blend adjoins the components at their pentagrams, theirby blending those out. Because in stiscu the pentagram had been a membran face (i.e. was accessable from both sides), that blend becomes a true toroid, i.e. the former sidtid's center becomes accessable from the outside.

Incidence matrix

20  * |  6   6  0 |  3  6  3  vertices of sidtid
 * 60 |  0   2  2 |  0  2  2  base vertices of stiscu
------+-----------+---------
 2  0 | 60   *  * |  1  1  0
 1  1 |  * 120  * |  0  1  1
 0  2 |  *   * 60 |  0  1  1
------+-----------+---------
 3  0 |  3   0  0 | 20  *  *  (red)    - trigs of sidtid
 2  2 |  1   2  1 |  * 60  *  (yellow) - squares of stiscu
 1  2 |  0   2  1 |  *  * 60  (blue)   - trigs of stiscu