Assertion: polyhedron's edge | /r/HasProperty | tangent
Facets:
value: to the unit sphere
type: LOCATION
value: to the faces
type: TRANSITIVE-OBJECT
Source sentences:
text: If all edges of a square pyramid (or any convex polyhedron) are tangent to a sphere so that the average position of the tangential points are at the center of the sphere, then the pyramid is said to be canonical, and it forms half of a regular octahedron.
text: E.g., t4Y4 gives a brick, but ct4Y4 gives a canonical version, i.e., all edges are tangent to the unit sphere, which in this case gives the cube.
text: all the edges are tangent to the unit sphere, the origin is the center of gravity of the points at which the edges touch the sphere, the faces are flat (i.e. the vertices of each face lie in some plane), but are not necessarily regular.
text: As for the canonical version of the 17 sided polyhedron, I can see that all the edges are tangent to the unit sphere and the faces flat, but it seems remarkable to me that all the tangent points have a center of gravity right at the center of the unit sphere.