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

English: A regular faced square pyramid with edge length 2, (& body height √2) (red). Its polar dual: a right square pyramid with base edge length √2, & its apex at infinity (blue). Their common (unit) intersphere (which is also the circumsphere of their intersection*): thin dotted great circles, great semicircles, & circle arcs (black). *Their intersection: half a quasiregular cuboctahedron (grey). And 3 orthonormal axes: straight arrows with marks for integers (black). Coordinates of the pyramid's vertices: S(0,0,√2), T(√2,0,0), U(0,√2,0), V(-√2,0,0), W(0,-√2,0). Coordinates of the original edges' midpoints: A(1/√2,0,1/√2), B(0,1/√2,1/√2), C(-1/√2,0,1/√2), D(0,-1/√2,1/√2), E(1/√2,1/√2,0), F(-1/√2,1/√2,0), G(-1/√2,-1/√2,0), H(1/√2,-1/√2,0). Coordinates of the dual's vertices: J("0,0,∞"), K(1/√2,1/√2,1/√2), L(-1/√2,1/√2,1/√2), M(-1/√2,-1/√2,1/√2), N(1/√2,-1/√2,1/√2).