This polyhedron was found in 2025 by B. Klein in reply to 28T-15sH-7gH

Because having axial heptagonal symmetry, the numeric values are much harder to derive algebraically. However the above given circumradius (and some further values too) get generally derived for [p,q,q]-acrohedra here by formula.

As abstract polyhedron 28T-15H-7sH is isomorphic to 28T-15sH-7gH, thereby replacing heptagons {7} by small heptagrams {7/2} and small heptagrams {7/2} by great heptagrams {7/3}.

Incidence matrix

7 * *  *  * * * |  2  2  0 0 0  0  0  0 0  0 |  2  2 0 0 0 0  [3,7,3/2,7/6]
* 7 *  *  * * * |  0  0  2 1 0  0  0  0 0  0 |  0  2 1 0 0 0  [3,7,7]
* * 7  *  * * * |  0  0  2 0 2  2  0  0 0  0 |  0  2 2 1 1 0  [3,7/6,3,7,7/2,7]
* * * 14  * * * |  1  0  0 0 0  0  1  1 0  0 |  1  1 0 0 1 0  [3,7/2,7/6]
* * *  * 14 * * |  0  1  0 0 0  0  1  0 1  1 |  1  1 0 0 1 1  [3,7,3,7/2]
* * *  *  * 7 * |  0  0  0 1 0  0  0  0 0  2 |  0  2 0 0 0 1  [3,7,7]
* * *  *  * * 7 |  0  0  0 0 0  2  0  2 0  0 |  0  2 0 0 2 0  [7,7/2,7/6,7/5]
----------------+----------------------------+--------------
1 0 0  1  0 0 0 | 14  *  * * *  *  *  * *  * |  1  1 0 0 0 0
1 0 0  0  1 0 0 |  * 14  * * *  *  *  * *  * |  1  1 0 0 0 0
0 1 1  0  0 0 0 |  *  * 14 * *  *  *  * *  * |  0  1 1 0 0 0
0 1 0  0  0 1 0 |  *  *  * 7 *  *  *  * *  * |  0  2 0 0 0 0  acting like a meridian
0 0 2  0  0 0 0 |  *  *  * * 7  *  *  * *  * |  0  0 1 1 0 0  acting like a parallel circle
0 0 1  0  0 0 1 |  *  *  * * * 14  *  * *  * |  0  1 0 0 1 0
0 0 0  1  1 0 0 |  *  *  * * *  * 14  * *  * |  1  0 0 0 1 0
0 0 0  1  0 0 1 |  *  *  * * *  *  * 14 *  * |  0  1 0 0 1 0
0 0 0  0  2 0 0 |  *  *  * * *  *  *  * 7  * |  0  0 0 0 1 1  acting like a parallel circle
0 0 0  0  1 1 0 |  *  *  * * *  *  *  * * 14 |  0  1 0 0 0 1
----------------+----------------------------+--------------
1 0 0  1  1 0 0 |  1  1  0 0 0  0  1  0 0  0 | 14  * * * * *  {3}
1 1 1  1  1 1 1 |  1  1  1 1 0  1  0  1 0  1 |  * 14 * * * *  {7}
0 1 2  0  0 0 0 |  0  0  2 0 1  0  0  0 0  0 |  *  * 7 * * *  {3}
0 0 7  0  0 0 0 |  0  0  0 0 7  0  0  0 0  0 |  *  * * 1 * *  {7} axis-orthogonal
0 0 1  2  2 0 2 |  0  0  0 0 0  2  2  2 1  0 |  *  * * * 7 *  {7/2}
0 0 0  0  2 1 0 |  0  0  0 0 0  0  0  0 1  2 |  *  * * * * 7  {3}