I'm finding rotational symmetries of a cube and have some difficulties with visualizing $120^\circ$ or $240^\circ$ rotations.
Any tips?
[Math] How to visualize a $120^\circ$ (or $240^\circ$) rotation of a cube about its body diagonal
geometryvisualization
Related Solutions
Only that you can place a regular tetrahedron in a regular cube. Vertices, for example, at $$ (1,1,1); \; \; (1,-1,-1); \; \; (-1,1,-1); \; \; (-1,-1,1). $$ Each pair should disagree in two coordinates, agree in one.
It is just the pythagorean theorem:
Best Answer
Do you see the cube in this figure?
Hint:
Projecting the cube on a plane orthogonal to the main diagonal $1-8$ you find a regular hexagon (you can see an explict construction at: Construct orthogonal projection for plane (matrix form)), and you can easily see the angles.