4D Toys1.8.1

"I am not sure that I've ever seen a more compelling 'show-don't-tell' educational tool than 4D Toys." -Ars Technica

What if you received a box filled with mysterious toys from a fourth spatial dimension?

. Playfully explore and marvel at beautiful shapes powered by a groundbreaking 4D+time physics system.
. Poke, throw, roll and watch as they disappear into a dimension you can't see.
. Get an intuitive feel for how four-dimensional objects behave:
. Become a child of the fourth dimension.

In this case the 4D is not time but a 4th dimension of space that works just like the first three dimensions we are familiar with. If you count time these toys are 5D. It turns out that the rules of how objects bounce, slide and roll around can be generalized to higher dimensions, and this unique toy lets you experience what that would look like.

Features:
. Over 130 beautiful interactive scenes to play with, with more to be added in updates.

. Groundbreaking 4D+Time Physics Engine that uses new mathematics created for this project.

. Multi-touch & Accelerometer support for rich interactivity.

. 2D/3D "Flatland" Interactive 10 Page Book/Explanation that teaches by analogy about a fourth spatial dimension.

. Special buttons: Anti-Gravity, Wireframe Projection, 4D Accelerometer and ability to export meshes for 3D printing.

Some things to do:

. Manage to fit the hypercube into the hyperhole!
. Use the 4D shapes as fancy, perfectly symmetric, fair dice that have 5, 8, 16, 24, or even 120 and 600 sides!
. Unbind Rings using the fourth dimension!
. Make a stack of 4D hypercubes and smash it!
. Set up an interesting path for a few 4D dominoes!
. Make levers that throw hypercubes into the fourth dimension!
. Use multitouch to "squeeze" out objects into the fourth dimension!
. Play in a 4D ball pit!
. See Tesseracts (i.e. 4D hypercubes) slide down slopes!
. etc...!

Version History Full Blog Post with Videos: https://4dtoys.com/mega/

1. Rotating your 3D slice arbitrarily in 4D

2. Projection of the 2D Faces of the 4D objects

3. Colored Projection of the 1D Lines of the 4D objects

4. A lot of structures made to play with “marbles” and roll them around

5. Scenes with Tesseracts that are fixed at a point but with a torque that keeps them rotating

6. The 1D line version of the 2D “Davinci” 4D Objects

7. A static Klein bottle with a sphere that you can roll inside

8. A 120 cell (faces) and a sphere together

9. Auto-Follow the last touched shape

(+ Quick performance fix for older devices) 1.8.1 03/15/2023 Full Blog Post with Videos: https://4dtoys.com/mega/

1. Rotating your 3D slice arbitrarily in 4D

2. Projection of the 2D Faces of the 4D objects

3. Colored Projection of the 1D Lines of the 4D objects

4. A lot of structures made to play with “marbles” and roll them around

5. Scenes with Tesseracts that are fixed at a point but with a torque that keeps them rotating

6. The 1D line version of the 2D “Davinci” 4D Objects

7. A static Klein bottle with a sphere that you can roll inside

8. A 120 cell (faces) and a sphere together

9. Auto-Follow the last touched shape 1.8 03/13/2023 Added the Klein Bottle!

See the complementary explanation video: https://4dtoys.com/klein

Also added:
- The 2D Loop as a helper explanation for the Klein bottle
- The "Spherinder Klein Bottle," a higher dimensional generalization of the Klein bottle.

Bug Fixes since 1.7:
- Fixed a bug where older devices would run out of memory loading the Klein Bottle. Any devices released before 2017 now loads a lower detail version instead. Email support@4dtoys.com with any issues. 1.7.1 12/19/2021 Added the Klein Bottle!

See the complementary explanation video: https://4dtoys.com/klein

Also added:
- The 2D Loop as a helper explanation for the Klein bottle
- The "Spherinder Klein Bottle," a 4D (5D?) generalization of the Klein bottle. 1.7 12/14/2021 New button: Wireframe Projections.

When enabled, the edges of objects are projected onto the current slice.

That means that no matter where the slice is, the edges of the objects will always be visible.

It's an "old school" way of displaying 4D objects which you may have seen before!

Try it in the 2D Levels!

I had fun going back to every level to check it out. It lets you see the movement of the objects even if you are not in the same slice. 1.6 12/15/2020 Added three buttons:

* Export Mesh: Exports a 3D mesh of what is currently visible on screen.

These meshes can then be 3D printed, etc… (Unfortunately 4D printing is not yet available in this universe :P).

Find the meshes in your Documents folder. (You can access it by connecting your iDevice to your computer and using Finder).

Note that Shapeways’ algorithm for filling the inside of meshes sadly fails on some of the coolest meshes like the Star Polychora from the last update, since they are filled with lots of polygons on the inside.

* Anti-Gravity: Creates an anti-gravity field that makes objects float. Besides the obvious coolness, this allows to see rotations that are unrestricted from the constraints of the collision with the ground.

* 4D Accelerometer: Swaps the forward/backward direction of the accelerometer with the 4th dimension.

That is, tilting your device toward/away from you will result in a force along the 4th dimension instead.
A new page of shapes has been added, with one new level for each button. Visiting each of these levels unlocks the corresponding buttons. Also, all special buttons are now gathered into a new menu button. This lays the groundwork for easily adding new features in future updates! 1.2 08/19/2020 Added 11 new star-like shapes that would look great hanging from or on top of your 4D Christmas Tree.

The Regular Star Polychora (or "Schläfli-Hess 4-polytopes"):
* Icosahedral 120-cell
* Small stellated 120-cell
* Great 120-cell
* Grand 120-cell
* Great stellated 120-cell
* Grand stellated 120-cell
* Great grand 120-cell
* Great icosahedral 120-cell
* Grand 600-cell
* And my *personal favorite*, the Great grand stellated 120-cell

Plus a Compount 5-Cell for good measure.

The Star Polychora are the 4D equivalent of the 2D Star Polygons. Star polygons can be made by extending the edges of polygons, until they meet outside of the polygon. For example the "Star of David" can be made by extending the edges of a Hexagon. This process of extending edges (or faces and cells in 3D or 4D) is called Stellation.

Warmest wishes for a Happy Holiday Season and a wonderful New Year! I felt the need to take a break from updating 4D Toys for a bit, but more updates will be coming next year! 1.1 12/30/2019 * iPhoneX screen support
* Minor bug fixes and improvements
* 14 new shapes:

- Rectified 120Cell
- Runcinated 120Cell
- Truncated 120Cell
- Rectified 600Cell
- Truncated 600Cell
- Omnitruncated Tesseract (Faces)
- BiTruncated 24Cell (Faces)
- Cantellated 24Cell (Faces)
- Runcinated 24Cell (Faces)
- Grand Antiprism (Faces)
- Biparabigyrated Cantellated Tesseract
- Bi-Icositetradiminished 600Cell
- Square Magnabicupolic Ring
- Castellated Rhombicosidodecahedral Prism 1.0.3 11/20/2017 The Gyrochoron Update
It turns out there exists 4D dice shapes with any number of sides, even primes! This update adds an assortment of over 30 new dice with sides such as 9, 13 and of course 42.

Also bug fixes. 1.0.2 07/14/2017 - Added 7 more shapes!
- Added 'Roll Button' to all dice shapes.

- Fixed an iOS 8 crash when clicking on non force touch devices.
- Fixed a crash on iPod 6th gen. 1.0.1 06/26/2017 - Properly supports iPhone 6+ and iPhone 7+ screen resolutions.
- Fixes a crash after loading on old devices. 1.00 06/04/2017 1.0 06/02/2017