the great stellated triacontahedron is the first dual polyhedron that begins this webpage. in spite of the apparent simplicity of its 30 rhombic faces, for me, it was the one of the hardest to model. It’s in the cover of one of my favourite books, Coxeter’s “Regular Polytopes”.
the great icosicosidodecahedron is the first concave semiregular polyhedron that I chose to begin this webpage. more will follow, as well as more detailed descriptions of these uniform polyhedra.
this webpage shows some of the Grasshopper definitions with which I explored the concept of uniform expansion of polytopes in 2D and 3D, devised by Alicia Boole Stott in 1905. the following is one of these definitions and it shows the expansion of the edges of the cube.
this one is a 3D model of the expansion of the edges of the pentagonal dodecahedron:
this webpage was completed on November 7, 2021 with interactive 3D models for all the 14 concave quasiregular polyhedra.
below, 3 examples of the resources found in this webpage: interactive 3D models of the great dodecahemicosahedron and the ditrigonal dodecadodecahedron and a video showing how to obtain the great ditrigonal icosidodecahedron from the pentagonal dodecahedron.
tessellating in 3D | tessellating with truncated octahedra:
expanding the edges of polyhedra | expanding the edges of the dodecahedron:
studying symmetries | transitivity of the pentagonal dodecahedron: