Angles in spherical pentagon tilings

Tilings of the Sphere by Congruent Pentagons III: Edge Combination $a^5$

“…Then α 2 , ǫ 2 determine (all the angles of) P 2 . By V δ,1 = δ 3 or δǫ 3 and the non-adjacency of β 5 , ǫ 5 , we have V δ,2 = δ 3 , and get P 6 , δ 5 , δ 6 . Then β 5 , δ 5 determine P 5 .…”

“…We would like to thank Mr. Hoiping Luk for the preliminary work [3] for Lemma 1, and for the understanding of the special tiling as the exotic twisting of earth map tiling.…”

Tilings of the Sphere by Edge Congruent Pentagons

“…In a subsequent paper [1], we will further consider the angles and study the full geometrical congruence. We also note that Luk and Yan [4,5] studied the numerical aspects of the angle congruence for general edge-to-edge spherical pentagonal tilings. Now we describe the results of this paper.…”

Angle Combinations in Spherical Tilings by Congruent Pentagons

“…For three angles α, β, γ at degree 3 vertices, we first list the full AVCs with α, β, γ as the only angles, then separately list the full AVCs with an angle δ appearing as αδ 3 , βδ 3 , γδ 3 , δ 4 or δ 5 .…”