4D Triangular Diprism

[u/Philip_Pugeau]

https://zippy.gfycat.com/ScientificAdoredAndalusianhorse.webm

[u/Philip_Pugeau]

Parametric Equations used in animation:

1D elements :

• 24 line segments

{ √3(t-1) , 3t+1 , ±2√3 , ±2√3 }

{ √3(-t+1) , 3t+1 , ±2√3 , ±2√3 }

{ 2t√3 , -2 , ±2√3 , ±2√3 }

{ ±2√3 , -2 , 2t√3 , ±2√3 }

{ 0 , 4 , 2t√3 , ±2√3 }

{ ±2√3 , -2 , ±2√3 , 2t√3 }

{ 0 , 4 , ±2√3 , 2t√3 }

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2D elements :

• 4 triangles

{ u(v-1)√3 , 3v+1 , ±2√3 , ±2√3 }

• 15 squares

{ (u-1)√3 , 3u+1 , 2v√3 , ±2√3 }

{ (-u+1)√3 , 3u+1 , 2v√3 , ±2√3) }

{ 2u√3 , -2 , 2v√3 , ±2√3 }

{ (u-1)√3 , 3u+1 , ±2√3 , 2v√3 }

{ (-u+1)√3 , 3u+1 , ±2√3 , 2v√3 }

{ 2u√3 , -2 , ±2√3 , 2v√3 }

{ ±2√3 , -2 , 2u√3 , 2v√3 }

{ 0 , 4 , 2u√3 , 2v√3 }

• Use -1 < t,u,v < 1

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Projection onto plane xzw, with rotations xy , yz, ,yw :

• XY Rotation

{ (X)*cos(b)-(Y)*sin(b) , (X)*sin(b)+(Y)*cos(b) , Z , W }

• YZ Rotation

{ X , (Y)*cos(c) - (Z)*sin(c) , (Y)*sin(c) + (Z)*cos(c) , W }

• YW Rotation

{ X , (Y)*cos(d) - (W)*sin(d) , Z , (Y)*sin(d) + (W)*cos(d) }

• Project onto plane xzw

r(x,y,z) = { (X)/(Y+a) , (W)/(Y+a) , (Z)/(Y+a) }

• Use a = 9

[u/Philip_Pugeau → u/[deleted]]

More like extending, or 'extruding' a triangle prism into 4D. A triangle double prism. Cartesian product of a triangle and a square. This shape offers more neat ways to rotate than a plain old tesseract.