Looking at it again, I think its a geodesic octahedron. Its a geodesic polygon instead of a regular polygon like a dodecahedron, not all faces are equal sized triangles, the ones in the center are right angled triangles instead of equilateral triangles, so you get a pattern of semi squares and semi hexagons. Thanks for indulging my love of polyhedra, and even more thanks for this incredible novel!
Yes I checked it and its a Class I Frequency 3, 0 Octahedral geodesic polygon. Naming gets messy quickly once you get to geodesics https://en.wikipedia.org/wiki/File:Octahedral_geodesic_polyhedron_03_00.svg
