4D D48

by mctrivia
  • Frosted Ultra Detail

    Matte translucent plastic that showcases fine and intricate details.

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It has come to my attention that though both sides of each face can be landed on they are still the same face when looking at in the 4th dimension. so i have made http://www.shapeways.com/model/167487/4d_d24.html to correct this.

This is a shadow of a 4 dimensional D48 Die. The shape is called a hyper cube. It is made up of 8 equally sized cubes with each face of each cube connected to a face of another cube. Since it is a shadow and not actually printed on a 4 dimensional printer there is some warping of geometry and a bit of thought is needed to see the 4 dimensional shape. Obviously it is impossible to roll the die and have it land on any sides other then 5,13,21,28,36, and 44 but even without trying it ended up being a fairly waited model.

To make it possible to print you will notice that each face has 2 numbers. the number that you can read correctly is the number for the side you are looking at. The number you can not read correctly is for the cube on the inside.

Hope you enjoy this unique die.


IN: 0.798 w x 0.798 d x 0.798 h
CM: 2.026 w x 2.026 d x 2.026 h


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2D surfaces in a 4D world would exist, sure, but they'd be hard to balance on. You could always fall off to one of the "sides". Stuff would fall off. I suppose you could tilt the die so the shadow has a different configuration, but I think you can't avoid having at least one cell "inside-out" (not sure, though). This is the best-known form for the shadow, though.
October 20, 2010, 3:22 am
It depends if you are rolling the die on a 2D surface or a 3d surface. This die is designed for a 4D universe where we still have 2d tables. I originally was going to design a D8 for a 3D surface but it is impossible to number more then 7 out of 8 of the sides as the outer cube is inverted in the shadow.
October 20, 2010, 3:14 am
This is such an awesome idea. Very cute. And naturally, one geeking deserves another: I would think that in 4D a die is very unlikely to land balanced on a face (it probably isn't even possible). It would be like a die in 3D landing on an edge. One would guess that dice are rolled onto 3D hyperplanar surfaces and would land on a cell (which would make this a d8). Fun fact: there are 5 convex regular polytopes (polyhedra) in 3D. There are 6 in 4D. In 5D and all higher, there are only three.
October 20, 2010, 3:07 am


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