A blog about satisfying my own curiosity.

Mostly about math, physics and computer science.
But also kanjis and modular origami.

Geometry : Interactive Galleries of Polyhedra

As a complement to the main viewer, here are galleries for the polyhedra organized by family.

Created on July 18th, 2022. Last update on July 23th, 2022.

Geometry : Possible polygonal arrangements around a vertex

The interest arose during some thinking about the arrangement of faces around the vertex of a polyhedron. Here is the solution in 2D.

Created on July 17th, 2022. Last update on July 17th, 2022.

Geometry : Prisms with Parquet Faces

The idea behind parquet polygons is to extend regular polygons to convex shapes made of them. Here, I will show what they look like and how to generate them. At the end, they will be turned into prisms to be viewed with the polyhedra viewer !

Created on June 27th, 2022. Last update on June 27th, 2022.

Geometry : Polyhedra Viewer using Three.js

Here is the full screen interactive viewer for polyhedra. I will use it to display all the polyhedra I have found over the internet or made by myself.

Created on June 26th, 2022. Last update on June 26th, 2022.

Rendering : Making and rendering the origami models

If you have taken a look at the graph of convex polyhedra with regular faces in this post, you could see that by hovering over a node, animations of the corresponding solid would be displayed. I could not use the glass rendering I had made for the origami models because it would have been too long to render for the 200+ solids in the graph. So I needed another approach. In this article I show how I made these simpler renders.

Created on February 11, 2019.

Geometry : Interactive network of the convex regular-faced polyhedra

Even though I have not explained anything about convex polyhedra with regular faces yet, I have decided to post this network first. It is a tool I have made to better visualize the construction relationship between the many solids.

Created on December 3rd, 2018. Last update on January 25, 2019.

Rendering : Making and rendering the origami models

Once I had made the stop motion animation, I figured out it would be interesting to make some rendering to achieve the same animation. I had used Blender before but only for its 3D modeling capabilities and I always wanted to learn to use it for proper rendering too. In my head, the project seemed simple, I needed the 3D model, to make a scene for it with lights, cool materials and stuff and to render it. As a beginner I faced many challenges but it was worth it.

Created on August 23, 2018. Last update on January 19, 2019.

Misc : Stopmotion

As you could see in the section about origamis, I have made some animated pictures of many of the polyhedra I have built. In this post, I will explain how I did it.

Created on August 22, 2018. Last update on January 12, 2019.

Origami part 4 : Johnson Deltahedra

Quite a long time later after making the rhombic polyhedra, I stumbled upon a book on mathematics the title of which I don't remember.

Created on August 22, 2018. Last update on January 2, 2019.

Origami part 3 : Rhombic Polyhedra

I found out about rhombic polyhedra with two videos. The first one is a video from standupmaths where he makes a rhombic Bilinski dodecahedron out of cardboard.

Created on August 22, 2018. Last update on January 2, 2019.

Origami part 2 : Platonic Solids and Colorization

In the Micmaths' video, the base polyhedra are the 5 platonic solids, namely: the tetrahedron, the cube (or hexahedron), the octahedron, the dodecahedron and the icosahedron.

Created on August 22, 2018. Last update on January 2, 2019.

Origami part 1 : Introduction

I found about modular origamis originally with a video on making a Menger's sponge out of business card \cite{origamimengersponge}. I become quickly interested in this method to build things out off paper cubes but my cubic realizations are for another article (future ref).

Created on August 22, 2018. Last update on January 2, 2019.

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