4-Dimensional Objects

[Tarril Wolfeye]

See here:

http://en.wikipedia.org/wiki/Polychoron

btw, the hypercube either has 8 "sides" (cubes) or 24 "sides" (squares), because each cube has 6 squares and shares his sides with another cube, therefore: 8 cubes x 6 sides / 2 = 24

Some of the regular polychorones a quite big: I wouldn't want to try rolling a thing with 120 sides, each side looking like a d12.

 

[Turanil]

This thread seems to point out that there is also gamers that actually don't want a rule-lite system, but all the contrary a much more complex one than 3.5...

 

[Conaill]

As Fieari already alluded to, it's not quite that easy.

Actually, if you want a 4D "die", you don't want just any extrusion into 4D. What you really want is a 4D equivalent of the platonic solids, aka regular polyhedra. So what you're after are the regular polychora. Cool name, huh?

A polychoron is a 4D polytope, and a polytope is just a generalisation of the sequence point - line segment - polygon - polyhedron - polychoron. The "surface" of each regular polychora consist of regular polyhedra. Luckily, you can find more info on these beasties on Mathworld. Apparently, there are only 16 regular polychora (just like there's only 5 platonic solids: d4, d6, d8, d12, d20).

For example, the hypercube is constructed by joining all the vertices of a cube with the corresponding vertices of a second cube offset in a 4th dimension. This polychoron is bounded by 8 cubes: the two on each end, and 6 more formed by connecting each side of the first cube to the second cube.

The other easy regular polychoron is the pentatope: take a tetrahedron (d4), and add one extra vertex equidistant from the other four nodes in 4D. It's pretty easy to see that the pentatope consists of 5 vertices, 10 edges, 10 triangles, and 5 tetrahedra...

Now... of course it all depends on how you want to roll these 4D dice! I would recommend a 4D table top, which means that the dice will come to rest on one of their polyhedra, rather than one of their polygons. Besides, a 4D table top also provides more space for sodas, charactersheets, etc.

 

[Whizbang Dustyboots]

Technically speaking, all dice are already in 4D. If they didn't have any measurable existence in time, we'd be unable to perceive them.

 

[Ravellion]

... Forgive me for drooling on the carpet. It's hard for me to keep my mouth closed (I feel like I am missing a chromosome).

Rav

 

[fafhrd]

... Forgive me for drooling on the carpet. It's hard for me to keep my mouth closed (I feel like I am missing a chromosome).

Rav

I wouldn't worry too much. This guy:

Conaill
Community Supporter

Join Date: Jan 2002
Location: NEW! Alameda, CA

Clearly works with nuclear wessels.

 

[the Jester]

nuclear wessels.

SNORT!

 

[tarchon]

This thread seems to point out that there is also gamers that actually don't want a rule-lite system, but all the contrary a much more complex one than 3.5...

Oh, so you want to talk about fractal polytopes...

 

[Stormrunner]

That is definitely a cool site. I just spent about three hours playing with it.
In particular if you look under Polyhedra, you can download cut-and-fold paper templates for all the dice shapes - including a d12 that doesn't use pentagons, several d24 shapes, a d48, several d60s...

Not that any of them will ever be useful, mind you, but they look cool.

 

[arscott]

As Fieari already alluded to, it's not quite that easy.

Actually, if you want a 4D "die", you don't want just any extrusion into 4D. What you really want is a 4D equivalent of the platonic solids, aka regular polyhedra. So what you're after are the regular polychora. Cool name, huh?

A polychoron is a 4D polytope, and a polytope is just a generalisation of the sequence point - line segment - polygon - polyhedron - polychoron. The "surface" of each regular polychora consist of regular polyhedra. Luckily, you can find more info on these beasties on Mathworld. Apparently, there are only 16 regular polychora (just like there's only 5 platonic solids: d4, d6, d8, d12, d20).

Yeah, but of those 16, only 6 are convex. the remainder are concave, and thus unsuitiple for rolling. These platonic hypersolids would be the d5, d8, d16, d24, d120, and d600.

of course, if we limited ourselved to platonic solids in our lowly three dimensional games, we wouldn't have a d10. And the d120 and d600 would probably be too much of a pain to manufacture (or roll, for that matter). so I'd say that our 4-D gaming friends use d5, d8, d10*, d16, and d24.

*or more accurately d(number of fingers)

my question is how could you make the d20 system work without a d20?