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This feels like a silly question, what am I missing:

I'm a 3D artist working on videogames. Sometimes I make 3D artworks like the ones here: http://samuelthomson.org/blog/2012/06/07/topologic-analogies-6-public-sphere-2/

Translating, rotating and scaling are fundamental to working in 3D in programs like blender, 3DSmax, Unity, etc.

In real life, if I pick up a banana I can easily rotate and translate it, but scaling feels impossible. What is the reason for this?

Are translation, rotation, and scale related on some deep fundamental level, in a similar way to angles on a triangle?

This is probably VERY wrong, but I think about things like a banana as a collection of atoms, and atoms as tiny little solar systems, and rotating it, I just fix a point of origin and rotate, and translating I pick a direction and...push. Anyway, rotating and translating feel like they belong in column A, but scaling feels like it belongs in column B, because it requires a point of origin AND a ...push (in a weird way in my mind) to get it how I want it to be.

And are hypercubes involved because they look like a small cube inside a scaled up cube?

Can anyone shed any light on this?

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    $\begingroup$ Are you familiar with linear algebra? The ideas of the rotation and scaling can be succinctly described as linear transformations of 3D space, which may be represented as $3 \times 3$ matrices. Translations can be expressed as well if you allow for affine transformations. $\endgroup$ – Brian Apr 27 at 23:45
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In real life, we can only perform proper rigid transformations, assuming the object we are transforming is solid. These are maps that preserve distances between points (and thus angles), as well as the handed-ness of objects (i.e., you can't turn an object into a mirror image of itself).

I'm not sure what you are getting at with your question about hypercubes, but they do not look like "a small cube inside a bigger cube" any more than a 3-D cube looks like a small square inside a bigger square.

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