New 4D Toys Update (iOS) (Steam VR & Mouse+KB)
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 Compound 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 this Hexagram (or “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!
4D Toys Version 1.1 Update on Steam
(Miegakure Update forthcoming)
(I also never posted here about the other updates, such as the gryochora: It turns out there exist 4D dice shapes with any number of sides, even primes! Added an assortment of over 30 new dice with sides such as 9, 13 and of course 42.)
Edit: comments were broken. fixed now.
Love the Stars! Would like to learn more about the gryochora, but googling it returned only this blog post, as does most of my research into 4D geometry.
Your pages and a page titled “4D Euclidean space” are some of the best resources in the area of hyper geometry.
Here is a link: http://www.polytope.net/hedrondude/dice4.htm
Cool thanks! I’ve been to that site, I forget about it.
Great to see an update. Would it be possible to add some kind of more precise rotations control to 4D toys? Being able to control rotations in all 4 axes using sliders or something would really help to better understand geometry of these objects. Also, fingers crossed for Miegakure update!
Yeah, I want to do more rotation on 4D Toys, but that is a lot more work than adding shapes!
Having the option some day to see 4D objects as 3D shadows instead of 3D slices would be awesome
This is definitely coming in next update.
🙂
Especially now that you have one of the regular compounds, I’d really like to see the other six, considering that Stella can only render one of them and they aren’t on Bowers’s site. They are:
3 tesseracts, with the same vertex and edge arrangement as the 24-cell.
3 16-cells, dual to the previous and also with the same vertex arrangement as the 24-cell.
2 24-cells, in dual orientation.
6 (2*3) tesseracts, constructed analogously to the previous.
6 (2*3) 16-cells, constructed analogously to the previous two.
120 (60*2) 5-cells, with the same vertex arrangement as the 120-cell.
I would love to do that. Do you have a link to a good reference with more specifics? That would make it happen faster.
Your best bet is probably the Polytope Wiki (https://polytope.miraheze.org/wiki/Main_Page).