Angle Combinations in Spherical Tilings by Congruent Pentagons

We develop a systematic method for computing the angle combinations in spherical tilings by angle congruent pentagons, and study whether such combinations can be realized by actual angle or geometrically congruent tilings. We get major families of angle or geometrically congruent tilings related to the platonic solids.Comment: 58 pages, 5 figure