Question

Show that a regular tetrahedron may be inscribed in a cube, and that the subgroup of Cube that preserves the tetrahe- dron is isomorphic to Tetra. (Query: How many such in- scribed tetrahedra are there?)

Answer 1

Ans Given that, may be insCnbed in a cube, and A yegulay tetahed xon the tetra hedadn Presesves that Cobe Subgoup of that the is isomarphic to Tetra. The cube has g verties. Take foJs of them which do not share any edge of the Cobe E Two opPosi te vextices of the top squoie two of the and ). bottom which chosen top vestices not below the ae vert ces of tetra hedaon yaJ vestices Nou considey this аче (0oking for ave edg es you wi nd that the Sia sin faces, jotning the selected vertice's Diagonas of the you will also fhnd that you have chopped off ' the Plane through it's Other fou vertices uith o thyee neighbouaing verti ces leaving behind the fou Cuts the foux aces of the UOepaj oatA