Great Dirhombicosidodecahedron ("Miller's Monster")

A detailed description of a paper model of the Great Dirhombicosidodecahedron ("Miller's Monster") presents the polyhedron's combinatorial and geometric data and highlights its unusual properties. The solid is uniform with vertex configuration (5/2.4.3.4.5/3.4.3/2.4)/2, 124 faces (24 pentagrams, 40 triangles, 60 squares), 240 edges, 60 vertices and 1,280 external facelets; its dual is the Great Dirhombicosidodecacron. It is the only uniform polyhedron with eight faces meeting at each vertex (two pentagrams, two triangles, four squares) and the only one with snub faces other than triangles (here, snub squares). All faces occur in coplanar pairs and the squares pass through the polyhedron’s centre.

The build log gives measured model dimensions (edge ≈ 21.6 cm, diameter ≈ 30.6 cm), explains that the nets printed to 42 A4 pages (10 red, 9 purple, 23 yellow), and shows stepwise assembly photographs and tips. Practical details include counts of recurring parts (e.g., sets of 12 and 20), use of tabs that can be glued from both sides, internal supports created and printed using faceting mode, and an assembly sequence recommendation: delay attaching the purple pentagram-arm pairs until late to simplify joining. Photographs illustrate intermediate stages and how pieces slot and glue together for the finished complex model.