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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:

expansion of the dodecahedron’s edges by veraviana on Sketchfab

Studying the concave quasiregular polyhedra

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.

great dodecahemicosahedron by vera viana on Sketchfab

ditrigonal dodecadodecahedron by vera viana on Sketchfab


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:


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