Posts tagged 'Platonic solids'

W.27 3D Planes, De Gua’s Quadrea Law & Platonic Dihedral Spreads

In 3D space over F, quadrance is Q(A_1, A_2) = dx^2 + dy^2 + dz^2, a right-corner tetrahedron satisfies De Gua’s Quadrea Theorem A_base = A_xy + A_yz + A_zx, and the dihedral (face) spreads of ALL FIVE regular Platonic solids—Tetrahedron (8/9), Cube (1), Octahedron (8/9), Icosahedron (4/9), and Dodecahedron (4/5)—are exact rational numbers in Q!