Peabodies of constant width

We describe a new family of 3-dimensional bodies constant width that we have called peabodies, obtained from the Reuleaux tetrahedron by replacing small neighborhood all six edges with sections an envelope spheres. This contains, in particular, two Meissner solids and body tetrahedral symmetry Robert’s body. Behind construction this lies classical notion confocal quadrics discussed, for example, Hilbert Cohn-Vossen their famous book. will study prove distances alternating sequence four points always satisfies simple equation use to our width.