File:Right square pyramid & its polar dual about their common intersphere.png

English: A right square pyramid with side/base edge length ratio: √2, i.e. with angle between base plane & side edge: 60°, (base edge length: 2(√3)(1+2√2)/7, side edge length: 2(√3)(4+√2)/7, & body height: 3(4+√2)/7) (red). Its polar dual: a right square pyramid with side/base edge length ratio: (3+√2)/2, (base edge length: √3, side edge length: (√3)(3+√2)/2, & body height: 3(1+√2)/2) (blue). Their common (unit) intersphere (which is also the circumsphere of their intersection*): thin dotted great circles & circle arcs (black). *Their intersection: half a distorted cuboctahedron (grey). And 3 orthonormal axes: straight arrows with marks for integers (black). Coordinates of the original pyramid's vertices: S(0,0,2), T((√3)(4+√2)/7,0,(2-3√2)/7), U(0,(√3)(4+√2)/7,(2-3√2)/7), V(-(√3)(4+√2)/7,0,(2-3√2)/7), W(0,-(√3)(4+√2)/7,(2-3√2)/7). Coordinates of the original side edges' points of tangency to the intersphere: A((√3)/2,0,1/2), B(0,(√3)/2,1/2), C(-(√3)/2,0,1/2), D(0,-(√3)/2,1/2). Coordinates of the original base edges' points of tangency to the intersphere, i.e. their midpoints: E((√3)(4+√2)/14,(√3)(4+√2)/14,(2-3√2)/7), F(-(√3)(4+√2)/14,(√3)(4+√2)/14,(2-3√2)/7), G(-(√3)(4+√2)/14,-(√3)(4+√2)/14,(2-3√2)/7), H((√3)(4+√2)/14,-(√3)(4+√2)/14,(2-3√2)/7). Coordinates of the dual pyramid's vertices: J(0,0,-(2+3√2)/2), K((√3)/2,(√3)/2,1/2), L(-(√3)/2,(√3)/2,1/2), M(-(√3)/2,-(√3)/2,1/2), N((√3)/2,-(√3)/2,1/2).