#mathy stuffy

[knotty-et-al]

Visualization of the Rubik's cube

[art-of-mathematics]

Today I went to the Technische Sammlungen Dresden with my friend, and it was very interesting!

Torus (mug) and genus-2 torus (Pretzel) (has a pretzel 2 or 3 holes? 3 actually??? )

Möbius strip:

[knotty-et-al]

Great stellated dodecahedron

For that Kepler-Poinsot-Polyhedron I started to draw an icosahedron and continued to add triangular pyramids as "hats" on top of each of the 20 triangular icosahedron faces.

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This is the Small Stellated Dodecahedron I drew a while back:

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How are the Dodecahedron, Icosahedron, Small and Great Stellated Dodecahedron related?

(Source)

Truncation of the Small Stellated Dodecahedron:

Truncation of the Great Stellated Dodecahedron:

[knotty-et-al]

Drawing a truncated cube and a cuboctahedron from a cube....

As for understanding truncation: You can imagine having a cheese cube and just cutting of the vertices...

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Truncated cubes and cuboctahedra are Archimedian solids.

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I used isometric dot paper.

[knotty-et-al]

Truncated dodecahedron

By cutting off the vertices of the dodecahedron you get the truncated dodecahedron.

This results in the 12 pentagonal faces of the dodecahedron turning into 12 dekagonal (10-gonal) and 20 triangular faces.

(As the dodecahedron has 20 vertices, truncation results in 20 triangular faces.)

[knotty-et-al]

Polytope info card of the Truncated Cuboctahedron

Today I finished this friend-shaped archimedian solid.

I drew the tiny drawing in the down right corner of the card and resized it with my printer.

The drawing:

I drew this Truncated cuboctahedron in an isometric projection and used my beloved isometric dot paper.

To start with the truncated cuboctahedron I started to draw a cube (with pencil).

Then I altered the cube by drawing a cuboctahedron in it (with pencil as well). I truncated th vertices of the cube like in the depiction below:

Then I altered the cuboctahedron drawing with another truncation - resulting in the truncated cuboctahedron shape.

[For clarification: I later erased the pencil lines of the cube and cuboctahedron, because it became messy and these lines were just there to help in the drawing process.

For the photo I laid pictures of a cube and cuboctahedron besides the truncated cuboctahedron drawing to show the similarity between these shapes - and present the principle of truncation visually.)

[knotty-et-al]

New challenge (to establish a daily routine): Creating one new polytope info card after breakfast - each day.

(That is the first page of the list of the polytopes I want to make. (92 Johnson solids will be very very much, and I have to stop myself from thinking about those many solids. but eeeh. we might approach it step by step... )

So, I started the polytope cards project some time in the summer of this year.

I already made all 5 platonic solids,

some regular 4-polytopes (the 4D platonic solids plus the 24-cell that has no 3D sibling),

and the first 4 archimedian solids.

Today I created the truncated octahedron card:

Yesterday I made the truncated tetrahedron card:

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The general template of the cards is as following:

This project is still in progress.

Furtherly I want to add:

General explanations/index cards/summaries

[art-of-mathematics]

Today's Tiny Tetrahedron

(artist of the colorful artwork in the background of the first photo is unknown)