6.AT.5. REGULAR FACED POLYHEDRA
O. Rausenberger. Konvexe pseudoreguläre Polyeder. Zeitschr. für math. und naturwiss. Unterricht 46 (1915) 135 142. Finds the eight convex deltahedra.
H. Freudenthal & B. L. van der Waerden. Over een bewering van Euclides [On an assertion of Euclid] [in Dutch]. Simon Stevin 25 (1946/47) 115 121. ??NYS. Finds the eight convex deltahedra -- ignorant of Rausenberger's work.
H. Martyn Cundy. "Deltahedra". MG 36 (No. 318) (Dec 1952) 263 266. Suggests the name "deltahedra". Exposits the work of Freudenthal and van der Waerden, but is ignorant of Rausenberger. Considers non convex cases with two types of vertex and finds only 17 of them. Considers the duals of Brückner's trigonal polyhedra.
Norman W. Johnson. Convex polyhedra with regular faces. Canad. J. Math. 18 (1966) 169 200. (Possibly identical with an identically titled set of lecture notes at Carleton College, 1961, ??NYS.) Lists 92 such polyhedra beyond the 5 regular and 13 Archimedean polyhedra and the prisms and antiprisms.
Viktor A. Zalgaller. Convex polyhedra with regular faces [in Russian]. Seminars in Mathematics, V. A. Steklov Mathematical Institute, Leningrad, vol. 2 (1967). ??NYS. English translation: Consultants Bureau, NY, 1969, 95pp. Gives details of computer calculations which show that Johnson's list is complete. Defines a notion of simplicity and shows that the simple regular faced polyhedra are the prisms, the antiprisms (excepting the octahedron) and 28 others. Names all the polyhedra and gives drawings of the simple ones.
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