Anatomy of a Cube - Cleve Moler on Mathematics and Computing
 

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A cube is the familiar three-dimensional solid with eight vertices, six faces and twelve edges. I have been working with cubes recently in posts about both the Menger sponge fractal and the 4-by-4 matrix from computer graphics.

Contents[URL="https://www.labfans.com/bbs/#1fa7f07c-be2a-44fe-a34a-0dc3e6672e06"]Vertices[/URL][URL="https://www.labfans.com/bbs/#83452c44-3a54-4a0c-b93a-d1ecc99b8ab5"]Edges[/URL][URL="https://www.labfans.com/bbs/#81261545-a0d3-467e-8dd8-b5ef3c2d2824"]Wireframe[/URL][URL="https://www.labfans.com/bbs/#11024e9e-fbab-4e1b-902e-fb283954f9f3"]Faces[/URL]VerticesCartesian coordinates, V, for the eight vertices of a cube can be generated from the binary representation of 0:7.

j = (0:7)'j = 0 1 2 3 4 5 6 7 k = dec2bin(j)k = 8×3 char array '000' '001' '010' '011' '100' '101' '110' '111' V = double(k-'0')V = 0 0 0 0 0 1 0 1 0 0 1

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