Platonic solid fractals and their complements

From the faces of its bounded three-dimensions, this fractal reduces itself infinitely towards an infinite number of empty "centers" contained within this finite three-dimensional space.From the "center" of the boundaries of this finite three-dimensional cube, this fractal expands itself infinitely towards the cube's faces without ever fully reaching them.


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Here is a paradox. Mathematically speaking, these two infinite fractals can reside in each other, occupying the same three-dimensional space, without any space remaining between them, without any overlap or intersection between them, and without any modification to their shapes.

The yellow fractal reduces infinitely. The blue fractal expands infinitely. Yet the sum of these two infinite fractals is a completely solid, finitely bounded cube!

Finity and infinity are one, residing perfectly in each other.

Fractals

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By the expression of a simple mathematical formula, a two-dimensional "fractal" is created. This fractal infinitely and indefinitely contracts and expands in an exactly repetitive manner to approximately "reach" an infinite and indefinite number of "emptinesses." The only differences in this fractal are in it sizes of scale, which expand and reduce without end.

Hyperbolic Orthogonal Dodecahedral Honeycomb

Bincuntracated Cubic Tiling

Fourth-Dimensional Hypercube

This is what a fourth-dimensional hypercube looks like as visualized from a three-dimensional perspective.

Hypercubes in other dimensions

The Platonic Solids

The Platonic Solids

Tetrahedron


The exact projection of a Tetrahedron onto a sphere




Hexadron (Cube)


The exact projection of a Hexahedron (Cube) onto a sphere



Octahedron


The exact projection of a Octahedron onto a sphere




Icosahedron


The exact projection of a Icosahedron onto a sphere




Dodecahedredon


The exact projection of a Dodecahedron onto a sphere


Higher Dimensions of the Platonic Solids
In the mid-19th century the Swiss mathematician Ludwig Schläfli discovered the four-dimensional analogues of the Platonic solids, called convex regular 4-polytopes. There are exactly six of these figures; five are analogous to the Platonic solids, while the sixth one, the 24-cell, has no lower-dimensional analogue.

In dimensions higher than four, there are only three convex regular polytopes: the simplex, the hypercube, and the cross-polytope. In three dimensions, these coincide with the tetrahedron, the cube, and the octahedron.

It's not about others

It is not the shortcomings of others, nor what others have done or not done that one should think about, but what one has done or not done oneself.
The Dhammapada, Verse 50