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# 1. Menger Sponge

1. Menger Sponge
1.2. cards needed
1.2.1. level 0
1.2.2. level 1
1.2.3. level 2

A Menger Sponge ist a fractal curve with a surface area approching \infty while the volume approches 0 for higher order Merger sponges.

This seemed interesting, so I built one out of paper.

Fold 72 sonobe:

Insert the individual sonobe together to form the merger sponge:

Next step: Build a level 2 menger sponge (left as an exercise for the reader).



## 1.1. using blank business cards

A sturdier variant can be build using blank business cards:



## 1.2. cards needed

The amount of cards needed can be calculated using one of the formulas described in A212596, for example


f(n) = 4 * (8^n + 2 * 20^n)



### 1.2.1. level 0

(cube)


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12 cards



### 1.2.2. level 1

(cube with a hole made out of cubes)


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192 cards



### 1.2.3. level 2

(cube with a hole made out of cubes with hole made out of cubes)


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3456 cards source


emile - 1722854449.384239s - generated using vokobe "0.1.3"