Compound of Fifteen 16-Cells

This model represents a 3-dimensional shadow of the regular compound of fifteen 16-cells.  This compound has the nice property that it shares the vertices with a regular 600-cell, much as the regular compound of 5 cubes is inscribed in the regular dodecahedron, with each vertex of the 600-cell occupied by a vertex of exactly one 16-cell.  This shape has pyritohedral symmetry (a group of order 24 generated by reflection symmetries across 3 mutually perpendicular planes, together with a 3-fold cyclic permuation of the 3 coordinate axes.)  Further, this 3-dimensional shadow has a 2-dimensional shadow whose symmetry has 10-fold rotation symmetry.