24-cell + Tetrakis Hexahedron
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This is a 24-cell, also known as a hyperdiamond, perspective projected such that the outer envelope forms a tetrakis…
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This is a 24-cell, also known as a hyperdiamond, perspective projected such that the outer envelope forms a tetrakis hexahedron. The 24-cell is the 6th platonic solid that only exists in 4 dimensions, and I think the tetrakis hexahedron is the most beautiful projection of this object into 3 dimensions, a Catalan solid with 24 triangular faces, reminiscent of the 24 octahedral cells.
Note that only 23/24 vertices and 88/96 edges are visible, because there is an overlapping vertex in the center, connected by 8 overlapping edges to the corners of the large cube.
See Matt Parker's video from 2015, on why the hyperdiamond is THE BEST: https://www.youtube.com/watch?v=oJ7uOj2LRso
If you do the same vertex-first projection orthographically (no perspective), you get a rhombic dodecahedron, so I've included one for reference. The rhombic dodecahedron and tetrakis hexahedron (along with their duals, the cuboctahedron and truncated octahedron) provide a glimpse into what this "missing" platonic solid might look like if it could exist in 3 dimensions. This "missing" platonic solid would be self-dual like the 24-cell, whereas these four solids are not.
Print with organic/tree supports at relatively low speed. Expect a LOT of trees but they're removable with side cutters.
Category: Math Art