Johnson solid

The Johnson - body are a class of geometric bodies.

Properties

Johnson - body are strictly convex polyhedra that are composed exclusively of regular polygons, but neither Platonic solids, Archimedean body, prisms are still anti- prisms. Together with the Catalan bodies is that the corners of a Johnson body are not identical. A special feature under the Johnson - bodies is the pseudo - Rhombicuboctahedron ( J37 ), whose vertices are indeed locally uniform, but not globally.

Norman Johnson in 1966 published a list of 92 such polyhedra, of which he accepted that it is complete. This assumption was proved by Wictor Salgaller 1969.

List

At a Johnson - body is often covered with Jn, where n is the number of the body in the following list. For example, the triangular dome J3.

In the following list E is the number of vertices, K is the number of edges, Fn is the number of n-sided surfaces and F: = F3 F4 F5 ... the number of all surfaces of the respective body.

Pyramids, domes and rotunda

Modified pyramids

Modified domes and rotunda

Advanced prisms

Modified platonic solids

Modified Archimedean body

Literature and Links

• Eric W. Weisstein: Johnson Solid. In: MathWorld (English).
• Johnson Solid ( with various graphics, engl. )

• Polyhedron
• Blackboard