#archimedian solid

[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]

Tiny hexagon-spiral booklet with friend-shaped friend shapes of joy (platonic and archimedean solids drawn in isometric projection)

Front- and backside:

Laying at a stone to make the hexagon-spiral booklet appear more plastic:

This booklet can be folded into a tiny hexagon with moderate thickness:

[knotty-et-al]

Polyhedra on dotted isometric paper

Drawing polyhedra on dotted isometric paper is so calming. One does not need to use a ruler or a compass. Instead one can just count dots to determine the length, and play around with the angles.

[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]

Truncations of the cube

This is what I have done with my spare shape drawings...

Depicted are different truncations of the cube - and the cube itself.

The polyhedra are (from left to right and from top to bottom)

- Cube

- Truncated cube (Cube's vertices get cut off to one third of each edge.)

- Cuboctahedron (Cube's vertices get cut off to a half of each edge.)

- Rhombicuboctahedron (Cuboctahedron's vertices get cut off to a half of each edge.)

Truncated Cuboctahedron (Cuboctahedron's vertices get cut off to a third of each edge.)

[knotty-et-al]

Truncated Icosahedron

when my brain becomes more functional and less exhausted again i would like to make some tutorials about how to draw polyhedra on isometric grid paper.

I enjoy drawing truncated solids, because you can literally draw one polyhedron into another and just erase the lines of the previous polyhedron.

[knotty-et-al]

Polytope card of the Truncated Icosidodecahedron