the latest

On 21 April 2022, presented the talk “Studying Polyhedra with Advanced Digital Tools” in the online Art and Math Seminar Spring in Kansas University. More info in this webpage.

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”.

great stellated triacontahedron by vera viana on Sketchfab

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.

great icosicosidodecahedron by vera viana on Sketchfab

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: