The angles in this tessellation are all either 60o or 120o. Each chevron is a concave hexagon which can be broken down into four equilateral triangles.
I stumbled upon the compound above while playing with facetings, starting with the rhombic triacontahedron. Here’s the compound’s dual.
I made these rotating models using Stella 4d, a program you can try for free at this website.
I made this by hiding the pentagons and triangles of a rhombicosidodecahedron, then putting the remaining faces, all squares, into “rainbow color mode.” I did this using Stella 4d: Polyhedron Navigator, which you can try for free right here.
This symmetrohedron’s regular faces are twelve pentagons, thirty octagons, and twenty triangles. Its irregular faces include sixty yellow isosceles trapezoids, as well as sixty blue isosceles trapezoids. That makes 182 faces in all.
I used Stella 4d: Polyhedron Navigator to make this, and you can try this program yourself, as a free trial download, at http://www.software3d.com/Stella.php.