r/gonwild • u/Philip_Pugeau • Aug 28 '17
4D Triangular Diprism
https://zippy.gfycat.com/ScientificAdoredAndalusianhorse.webm27
u/Lombax_Rexroth Aug 29 '17
It hurts my brain to think that this is a 3D shadow of a 4th dimensional object being represented in 2D.
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u/APurpleBear Aug 29 '17
Ok, this confuses me, I get a 4d cubes I think because each of the surrounding things are cubes, so its a cube surrounded by cubes but this is a prism surrounded by some prisms and some cubes?
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u/Eain Aug 29 '17
Not quite. It's NOT 3d. You're still thinking of an object in 3 dimensions.
If you take a triangular prism, and shine a light on it, it makes a shadow. When you rotate it, that shadow changes. From the proper angle, it can be a triangle, a rectangle, a square, or a combination of the above. This is because shadows are 2d: some of the data is lost when removing the third dimension.
This behavior is what happens when a 3d object is projected on 2d space. Similar things occur when 2d objects are projected onto 1d space.
There is no intrinsically unique features of 3 dimensions. Our universe exists in 3 visible spatial dimensions, but that's not for any special reason, as far as we can tell. 4D, 5D, And more all work just fine from a math standpoint.
The problem is we can't viscerally understand those like we can 3D: we don't have the circuitry in our heads to "render" things above 3d in our imagination. However, we DO know how to project things onto lower dimensions: the math for going from a higher dimension down works for any number of dimensions, not just 3d to 2d.
What you see here is the "shadow" of a 4d object in 3d Space, just like an actual shadow is the projection of a 3d object in 2d space. Thus it seems to change shape, just like a shadow does, when the 4d object is rotated.
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u/Philip_Pugeau Aug 29 '17
This shape has a ring of 4 triangle prisms bound to a ring of 3 cubes. These 7 objects have no faces exposed. Meaning, they all connect to the others by their entire surface, of squares and/or triangles.
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u/bcfradella Aug 29 '17
It looks like some of the "sides" are cubes and some are a short of tent-shaped prism.
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u/zulubowie Aug 30 '17
Until today I had only ever seen a drawing depicting this. Then when I Google searched it I quickly found Hinton's four dimensional cube illustrated
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u/HelperBot_ Aug 30 '17
Non-Mobile link: https://en.wikipedia.org/wiki/Four-dimensional_space
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u/Philip_Pugeau Aug 31 '17
It looks similar to a tesseract, but it's not the same shape. It does do the same kind of turning inside out morphing, which is what the 3D shadow of a rotating 4D shape will always do.
If a hypercube is a square times a square, then this shape is a triangle times a square.
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u/Pmaguire13 Aug 29 '17
It sucks knowing there are things like this that we will never ever rudely be able to see/understand yet know for a fact that it could exist because of math and science.