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knotty-et-al · 6 months

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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.)

#polytopes #polytope #polyhedra #polyhedron #cuboctahedron #truncated cuboctahedron #archimedian solid #archimedian solids #geometry #math #mathy stuffy #knottys math #polytope info cards #math art #mathy #mathematics

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knotty-et-al · 6 months

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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:

- - -- ---

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

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knotty-et-al · 5 months

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Polytope card of the Truncated Icosidodecahedron

#damn - drawing dat graph on a tiny 3x3cm square was challenging #truncated icosidodecahedron #archimedian solid #archimedian solids #polytope cards #polytope info cards #polyhedron #polyhedra #polyhedron info cards #geometry #math #mathematics #mathy #knottys math #info cards

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knotty-et-al · 6 months

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Polytope info card of the Snub Cube

Today's shape was the archimedian solid "Snub cube".

The snub cube has 38 faces in total - 6 square faces and 32 triangular faces.

It has 60 edges and 24 vertices.

Each vertex is met by 4 triangle faces and 1 square face.

A snub cube is an alteration of a truncated cuboctahedron.

The drawing:

For the isometric projection drawing I started with a truncated cuboctahedron, and continued to alter the truncated cuboctahedron's octagonal faces into square faces.

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knotty-et-al · 5 months

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Polytope card of the Icosidodecahedron

#polytope info cards #polytope #polytopes #polyhedra #polyhedron #icosidodecahedron #archimedian solid #geometry #shapes #shape #info cards #polytope cards

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knotty-et-al · 5 months

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Polytope card of the Truncated Dodecahedron

For drawing the graph I started with drawing the graph of a dodecahedron, but exchanged every one of the 20 vertices/dots with a triangle (alias three dots and three edges).

(Graph/Schlegel diagram of the dodecahedron: )

#polytope info cards #polytope #polytopes #polyhedra #polyhedron #knottys math #geometry #archimedian solid #truncated dodecahedron

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knotty-et-al · 6 months

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Polytope info card of the Rhombicuboctahedron

#rhombicuboctahedron #archimedian solid #polytopes #polyhedra #polytope info cards #geometry #math love #math #mathematics #knottys math #mathy stuffy #polyhedron #graph #graph theory

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knotty-et-al · 5 months

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Polytope card of the Truncated Icosahedron

It is the shape of common footballs.

#polyhedra #polytope cards #polytope inro cards #knottys math #geometry #math #info cards #polyhedron #archimedian solid #truncated icosahedron #shapes #shape

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