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The short diagonal HH of the hexagons ((H,h,h)²) is 5/3 edge units.
Their acute angle is r = arccos(-1/3) = 109.471221°, the obtuse angle thus is H = arccos(-7/9) = 141.057559°.

This polyhedron also occurs as convex hull of a strut composed of 32 octs and 6 squippies.

Incidence matrix

24  * |  2  2  0 | 1  2  1 0  [3,4,3,H]
 * 24 |  0  2  2 | 0  1  2 1  [(3,h)2]
------+----------+----------
 2  0 | 24  *  * | 1  1  0 0
 1  1 |  * 48  * | 0  1  1 0
 0  2 |  *  * 24 | 0  0  1 1
------+----------+----------
 4  0 |  4  0  0 | 6  *  * *
 2  1 |  1  2  0 | * 24  * *
 2  4 |  0  4  2 | *  * 12 *  ((H,h,h)2)
 0  3 |  0  0  3 | *  *  * 8