Calculations for a 5-frequency
Icosahedral Geodesic Patch
with Edge Length 1

Vertices

Vertexxyz
(0,0)000.95106
(0,1)0.15171-0.110220.93239
(1,0)0.151710.110220.93239
(0,2)0.32116-0.233340.86424
(1,1)0.3312900.89149
(2,0)0.321160.233340.86424
(0,3)0.48174-0.350010.74157
(1,2)0.51365-0.12440.79069
(2,1)0.513650.12440.79069
(3,0)0.481740.350010.74157
(0,4)0.60683-0.440890.5847
(1,3)0.66258-0.24070.63841
(2,2)0.6848700.65989
(3,1)0.662580.24070.63841
(4,0)0.606830.440890.5847
(0,5)0.68819-0.50.42533
(1,4)0.75854-0.330670.46881
(2,3)0.80291-0.116670.49622
(3,2)0.802910.116670.49622
(4,1)0.758540.330670.46881
(5,0)0.688190.50.42533

Chord Lengths

ChordsCountLength
(0,0)-(0,1) (0,0)-(1,0) (0,4)-(0,5) (0,5)-(1,4) (4,0)-(5,0) (4,1)-(5,0)60.18845
(0,1)-(1,1) (1,0)-(1,1) (0,4)-(1,3) (3,1)-(4,0) (1,3)-(1,4) (3,1)-(4,1)60.21464
(0,1)-(0,2) (1,0)-(2,0) (0,3)-(0,4) (3,0)-(4,0) (1,4)-(2,3) (3,2)-(4,1)60.22026
(0,1)-(1,0) (0,4)-(1,4) (4,0)-(4,1)30.22045
(0,2)-(1,2) (0,3)-(1,2) (2,0)-(2,1) (2,1)-(3,0) (2,2)-(2,3) (2,2)-(3,2)60.23309
(0,2)-(0,3) (2,0)-(3,0) (2,3)-(3,2)30.23334
(0,2)-(1,1) (1,1)-(2,0) (0,3)-(1,3) (3,0)-(3,1) (1,3)-(2,3) (3,1)-(3,2)60.23514
(1,1)-(1,2) (1,1)-(2,1) (1,2)-(1,3) (1,3)-(2,2) (2,1)-(3,1) (2,2)-(3,1)60.24268
(1,2)-(2,1) (1,2)-(2,2) (2,1)-(2,2)30.24879

Subface Definition

VerticesDirection Coefficients
ABC
(0,0) (0,1) (1,0)0.0041200.03344
(0,1) (0,2) (1,1)0.01255-0.005310.04079
(0,1) (1,0) (1,1)-0.009020-0.03959
(0,2) (0,3) (1,2)0.02195-0.01180.03995
(0,2) (1,1) (1,2)-0.020130.00599-0.04381
(0,3) (0,4) (1,3)0.02652-0.015460.03011
(0,3) (1,2) (1,3)-0.028640.01217-0.03731
(0,4) (0,5) (1,4)0.02442-0.014750.01793
(0,4) (1,3) (1,4)-0.029120.01461-0.02423
(1,0) (1,1) (2,0)0.012550.005310.04079
(1,1) (1,2) (2,1)0.0250800.04537
(1,1) (2,0) (2,1)-0.02013-0.00599-0.04381
(1,2) (1,3) (2,2)0.03416-0.006590.03844
(1,2) (2,1) (2,2)-0.032540-0.0426
(1,3) (1,4) (2,3)0.03383-0.010160.02453
(1,3) (2,2) (2,3)-0.036890.00618-0.03101
(2,0) (2,1) (3,0)0.021950.01180.03995
(2,1) (2,2) (3,1)0.034160.006590.03844
(2,1) (3,0) (3,1)-0.02864-0.01217-0.03731
(2,2) (2,3) (3,2)0.0381900.02754
(2,2) (3,1) (3,2)-0.03689-0.00618-0.03101
(3,0) (3,1) (4,0)0.026520.015460.03011
(3,1) (3,2) (4,1)0.033830.010160.02453
(3,1) (4,0) (4,1)-0.02912-0.01461-0.02423
(4,0) (4,1) (5,0)0.024420.014750.01793

Fastening Angles

VerticesEdgeFastening Angle
radiansdegrees
(0,0) (0,1) (1,0)(0,0) (0,1)1.4989485.88288
(0,1) (1,0)1.5319587.77434
(1,0) (0,0)1.4989485.88288
(0,1) (0,2) (1,1)(0,1) (0,2)1.499185.89196
(0,2) (1,1)1.5138586.73705
(1,1) (0,1)1.4944885.62737
(0,1) (1,0) (1,1)(0,1) (1,0)1.5081986.41266
(1,0) (1,1)1.5027886.10282
(1,1) (0,1)1.5027886.10282
(0,2) (0,3) (1,2)(0,2) (0,3)1.4995785.91926
(0,3) (1,2)1.4993585.90625
(1,2) (0,2)1.4993585.90625
(0,2) (1,1) (1,2)(0,2) (1,1)1.4964685.74076
(1,1) (1,2)1.5035986.14942
(1,2) (0,2)1.4946785.6383
(0,3) (0,4) (1,3)(0,3) (0,4)1.499185.89196
(0,4) (1,3)1.4944885.62737
(1,3) (0,3)1.5138586.73705
(0,3) (1,2) (1,3)(0,3) (1,2)1.4946785.6383
(1,2) (1,3)1.5035986.14942
(1,3) (0,3)1.4964685.74076
(0,4) (0,5) (1,4)(0,4) (0,5)1.4989485.88288
(0,5) (1,4)1.4989485.88288
(1,4) (0,4)1.5319587.77434
(0,4) (1,3) (1,4)(0,4) (1,3)1.5027886.10282
(1,3) (1,4)1.5027886.10282
(1,4) (0,4)1.5081986.41266
(1,0) (1,1) (2,0)(1,0) (1,1)1.4944885.62737
(1,1) (2,0)1.5138586.73705
(2,0) (1,0)1.499185.89196
(1,1) (1,2) (2,1)(1,1) (1,2)1.4939385.59562
(1,2) (2,1)1.4996285.92203
(2,1) (1,1)1.4939385.59562
(1,1) (2,0) (2,1)(1,1) (2,0)1.4964685.74076
(2,0) (2,1)1.4946785.6383
(2,1) (1,1)1.5035986.14942
(1,2) (1,3) (2,2)(1,2) (1,3)1.4939385.59562
(1,3) (2,2)1.4939385.59562
(2,2) (1,2)1.4996285.92203
(1,2) (2,1) (2,2)(1,2) (2,1)1.4945585.63148
(2,1) (2,2)1.4945585.63148
(2,2) (1,2)1.4945585.63148
(1,3) (1,4) (2,3)(1,3) (1,4)1.4944885.62737
(1,4) (2,3)1.499185.89196
(2,3) (1,3)1.5138586.73705
(1,3) (2,2) (2,3)(1,3) (2,2)1.5035986.14942
(2,2) (2,3)1.4946785.6383
(2,3) (1,3)1.4964685.74076
(2,0) (2,1) (3,0)(2,0) (2,1)1.4993585.90625
(2,1) (3,0)1.4993585.90625
(3,0) (2,0)1.4995785.91926
(2,1) (2,2) (3,1)(2,1) (2,2)1.4996285.92203
(2,2) (3,1)1.4939385.59562
(3,1) (2,1)1.4939385.59562
(2,1) (3,0) (3,1)(2,1) (3,0)1.4946785.6383
(3,0) (3,1)1.4964685.74076
(3,1) (2,1)1.5035986.14942
(2,2) (2,3) (3,2)(2,2) (2,3)1.4993585.90625
(2,3) (3,2)1.4995785.91926
(3,2) (2,2)1.4993585.90625
(2,2) (3,1) (3,2)(2,2) (3,1)1.5035986.14942
(3,1) (3,2)1.4964685.74076
(3,2) (2,2)1.4946785.6383
(3,0) (3,1) (4,0)(3,0) (3,1)1.5138586.73705
(3,1) (4,0)1.4944885.62737
(4,0) (3,0)1.499185.89196
(3,1) (3,2) (4,1)(3,1) (3,2)1.5138586.73705
(3,2) (4,1)1.499185.89196
(4,1) (3,1)1.4944885.62737
(3,1) (4,0) (4,1)(3,1) (4,0)1.5027886.10282
(4,0) (4,1)1.5081986.41266
(4,1) (3,1)1.5027886.10282
(4,0) (4,1) (5,0)(4,0) (4,1)1.5319587.77434
(4,1) (5,0)1.4989485.88288
(5,0) (4,0)1.4989485.88288