Turns out that rotating the tesseract to the optimal position can be done in the following fashion:

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Turns out that rotating the tesseract to the optimal position can be done in the following fashion:

- gonegahgah
- Tetronian
**Posts:**439**Joined:**Sat Nov 05, 2011 3:27 pm**Location:**Queensland, Australia

There is an interesting observation form the results.

I had already guessed the more obvious result...

A regular cube held with a corner point towards us can be rotated around the z-axis (forward).

This gives 360° (or a circle) of possible cube views through the one corner in its optimal view.

I had also realised that this would mean that a tesseract has a sphere of optimal views.

That was just a simple extension.

What I didn't realise is that this will effect the results of rotation.

Rotating the x-w planes alone does not appear to give the same 3D slice shape at 0°, 90°, 180° & 270°.

I was expecting the same shape just with different colours.

It seems that you have to do some sort of tumble between the w-x-y planes to achieve that!

Is that correct?

I had already guessed the more obvious result...

A regular cube held with a corner point towards us can be rotated around the z-axis (forward).

This gives 360° (or a circle) of possible cube views through the one corner in its optimal view.

I had also realised that this would mean that a tesseract has a sphere of optimal views.

That was just a simple extension.

What I didn't realise is that this will effect the results of rotation.

Rotating the x-w planes alone does not appear to give the same 3D slice shape at 0°, 90°, 180° & 270°.

I was expecting the same shape just with different colours.

It seems that you have to do some sort of tumble between the w-x-y planes to achieve that!

Is that correct?

Last edited by gonegahgah on Sat Mar 17, 2018 8:32 am, edited 1 time in total.

- gonegahgah
- Tetronian
**Posts:**439**Joined:**Sat Nov 05, 2011 3:27 pm**Location:**Queensland, Australia

I'm guessing that it would entail each cube 'face' to achieve a one third rotation along their horizontally back-forward-most axis as an overlay to the tesseract itself going through a one quarter rotation?

I wonder if that is easy to calculate, or not? One because the cube one third rotation would need to be relative to the viewer and because its axis would change angles through the process...

We already know it takes a one third rotation to get an identical forward shape cube (colours rotated) that is rotating in best orientation. That is because their are three faces toward front and three towards the back.

With a tesseract in best orientation there are four cube faces at the front and four cube faces at the back. Which is why I assume it takes a quarter rotation to get back to the original shape (if coupled with the cube rotations).

But the rotations need to be simultaneously overlaid otherwise the cube faces would overshoot their alignment; I'm guessing?

I wonder if that is easy to calculate, or not? One because the cube one third rotation would need to be relative to the viewer and because its axis would change angles through the process...

We already know it takes a one third rotation to get an identical forward shape cube (colours rotated) that is rotating in best orientation. That is because their are three faces toward front and three towards the back.

With a tesseract in best orientation there are four cube faces at the front and four cube faces at the back. Which is why I assume it takes a quarter rotation to get back to the original shape (if coupled with the cube rotations).

But the rotations need to be simultaneously overlaid otherwise the cube faces would overshoot their alignment; I'm guessing?

- gonegahgah
- Tetronian
**Posts:**439**Joined:**Sat Nov 05, 2011 3:27 pm**Location:**Queensland, Australia

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