My webpage with the concave quasiregular polyhedra is finally complete, with interactive 3D models for each of the 14:

• 01 great dodecadodecahedron
• 02 great icosidodecahedron
• 03 small ditrigonal icosidodecahedron
• 04 great ditrigonal icosidodecahedron
• 05 ditrigonal dodecadodecahedron
• 06 tetrahemihexahedron
• 07 octahemioctahedron
• 08 cubohemioctahedron
• 09 small icosihemidodecahedron
• 10 small dodecahemidodecahedron
• 11 great dodecahemicosahedron
• 12 small dodecahemicosahedro
• 13 great dodecahemidodecahedron
• 14 great icosihemidodecahedron.

The following is #11, the great dodecahemicosahedron:

great dodecahemicosahedron by vera viana on Sketchfab

Geometric and Aesthetic Concepts Based on Pentagonal Structures, authored by Cornelie Leopold, Academic Director in FATUK – Faculty of Architecture TUKaiserslautern, Germany

In this webpage, I included videos that explain how to model the first 5 concave quasiregular polyhedra and, in some cases, 3D models. The following is one of them:

For the first video on the subject of symmetry, a grasshopper definition meant to explain rotational symmetry with the pentagonal dodecahedron.

My doctoral thesis “Aplicações Didácticas sobre Poliedros para o Ensino da Geometria” (Didactic Applications on Polyhedra for the Teaching of Geometry) is available online in this link.

Some of its didactic applications will be included in this website (the ones available are found in this webpage , this one and also this). I will publish some more as soon as I have the time 🙂

The webpage concerning the convex semiregular polyhedra includes tutorials meant to show how to model:

• the truncated tetrahedron from the regular tetrahedron;
• the truncated cube from the cube;
• the truncated octahedron from the regular octahedron;
• the truncated octahedron from the cube.
• (more coming soon)

The webpage with tutorials on how to model the cuboctahedron and the icosidodecahedron is finished and may be found in the upper menu or here. Comments and suggestions are always welcomed.

The Conference of the International Society for the Interdisciplinary Study of Symmetry, focusing on “Symmetry, Structure, and Information” is scheduled as a Contributing Event to the IS4SI 2021, the annual Summit of the International Society for the Study of Information (IS4SI). This Summit will be held online between the 12th and the 19th of September, 2021.

The Call for Submissions of Abstracts is now open. Submissions can be sent until the until 1st of May 2021, to any of the members of the Organizing Committee listed below. More information is available here.

ORGANIZING COMMITTEE:

Co-chairs:

• Denes NAGY (President of the International Society for the Interdisciplinary Study of Symmetry) snagydenes@gmail.com
• Marcin J. SCHROEDER (Tohoku University, Japan) mjs@gl.aiu.ac.jp
• Vera VIANA (Faculty of Architecture of the University of Porto,Portugal) veraviana@veraviana.net

Members:

• Jean-Yves BÉZIAU (University of Brazil, Rio de Janeiro) jyb.logician@gmail.com
• Ferenc FRIEDLER (Széchenyi István University, Győr, Hungary) f.friedler@gmail.com
• Ted GORANSON (The Australian National University) tedgoranson@mac.com
• Ioannis VANDOULAKIS (Hellenic Open University,School of Humanities, Greece) i.vandoulakis@gmail.com
• Takashi YOSHINO (Department of Mechanical Engineering, Toyo University) tyoshino@toyo.jp

(updated in 09.02.2021)

Including all the subjects conceived for this site is an ongoing project that will take quite some time to accomplish, so I will detail below those which I consider to be complete (although any of them may be prone to changing):

• modelling:
  • the convex semiregular polyhedra (1 tutorial)
  • the convex quasiregular polyhedra (3 tutorials)
  • the convex regular polyhedra (4 tutorials)
• expanding | the edges of polyhedra:
  • snubbing the cube onto the cuboctahedron (1 video)
• tessellating:
  • in 3D (1 video)
• exploring | theorems:
  • Napoleon’s theorem (3 dynamic and step-by-step applets)
• exploring | plane curves:
  • curves (2 dynamic applets)
  • conics (10 step-by-step constructions, involving circles and ellipses)
• exploring | plane polygons:
  • triangles (8 step-by-step constructions)
  • quadrangles (7 step-by-step constructions)
  • regular pentagon (5 step-by-step constructions)
  • regular hexagon (4 step-by-step constructions)
  • regular octagon (3 step-by-step constructions)
  • regular decagon (2 step-by-step constructions)

I will include more links as soon as I finish them. Thank you for your understanding, and for your interest.

Há várias páginas e conteúdos do meu site em português que não estão, actualmente, acessíveis. O url veraviana.net direcciona-vos para o site que estou a construir mas, gradualmente, as páginas escritas em português voltarão a estar disponíveis. Consultem por favor esta página para saberem quais.

Os links para os livros geogebra com as contruções passo-a-passo e em movimento são os seguintes:

• construções interactivas
• construções de geometria plana (passo-a-apasso)
• exercícios de geometria descritiva (passo-a-passo)
• curvas
• theorems

muito obrigada pela compreensão.