== A list of Schwarz triangles ===== Möbius triangles for the sphere ===Schwarz triangles with whole numbers, also called Möbius triangles, include one 1-parameter family and three exceptional cases:# ["p",2] or ("p" 2 2) – Dihedral symmetry,# [3,3] or (3 3 2) – Tetrahedral symmetry,# [4,3] or (4 3 2) – Octahedral symmetry,# [5,3] or (5 3 2) – Icosahedral symmetry,=== Schwarz triangles for the sphere by density ===The Schwarz triangles ("p" "q" "r"), grouped by density:=== Triangles for the Euclidean plane ===Density 1:#(3 3 3) – 60-60-60 (equilateral)#(4 4 2) – 45-45-90 (isosceles right)#(6 3 2) – 30-60-90#(2 2 ∞) - 90-90-0 "triangle"Density 2:#(6 6 3/2) - 120-30-30 triangleDensity ∞:#(4 4/3 ∞)#(3 3/2 ∞)#(6 6/5 ∞)=== Triangles for the hyperbolic plane ===Density 1:*(2 3 7), (2 3 8), (2 3 9) ... (2 3 ∞)*(2 4 5), (2 4 6), (2 4 7) ... (2 4 ∞)*(2 5 5), (2 5 6), (2 5 7) ... (2 5 ∞)*(2 6 6), (2 6 7), (2 6 8) ... (2 6 ∞)*(3 3 4), (3 3 5), (3 3 6) ... (3 3 ∞)*(3 4 4), (3 4 5), (3 4 6) ... (3 4 ∞)*(3 5 5), (3 5 6), (3 5 7) ... (3 5 ∞)*(3 6 6), (3 6 7), (3 6 8) ... (3 6 ∞)*(∞ ∞ ∞)Density 2:*(3/2 7 7), (3/2 8 8), (3/2 9 9) ... (3/2 ∞ ∞)*(5/2 4 4), (5/2 5 5), (5/2 6 6) ... (5/2 ∞ ∞)*(7/2 3 3), (7/2 4 4), (7/2 5 5) ... (7/2 ∞ ∞)*(9/2 3 3), (9/2 4 4), (9/2 5 5) ... (9/2 ∞ ∞)Density 3:*(2 7/2 7), (2 9/2 9), (2 11/2 11) ...Density 4:*(7/3 3 7), (8/3 3 8), (3 10/3 10), (3 11/3 11) ...Density 6:*(7/4 7 7), (9/4 9 9), (11/4 11 11) ...Density 10:*(3 7/2 7)The (2 3 7) Schwarz triangle is the smallest hyperbolic Schwarz triangle, and as such is of particular interest.
Vrednost 2 pomeni pravi kot.