Calculations for a 4-frequency
Icosahedral Geodesic Patch
with Edge Length 1

Vertices

Vertex	x	y	z
(0,0)	0	0	0.95106
(0,1)	0.19324	-0.1404	0.92057
(1,0)	0.19324	0.1404	0.92057
(0,2)	0.40451	-0.29389	0.80902
(1,1)	0.42533	0	0.85065
(2,0)	0.40451	0.29389	0.80902
(0,3)	0.57971	-0.42119	0.62533
(1,2)	0.63799	-0.15451	0.68819
(2,1)	0.63799	0.15451	0.68819
(3,0)	0.57971	0.42119	0.62533
(0,4)	0.68819	-0.5	0.42533
(1,3)	0.77295	-0.28079	0.47771
(2,2)	0.80902	0	0.5
(3,1)	0.77295	0.28079	0.47771
(4,0)	0.68819	0.5	0.42533

Chord Lengths

Chords	Count	Length
(0,0)-(0,1) (0,0)-(1,0) (0,3)-(0,4) (0,4)-(1,3) (3,0)-(4,0) (3,1)-(4,0)	6	0.24079
(0,1)-(1,1) (1,0)-(1,1) (0,3)-(1,2) (2,1)-(3,0) (1,2)-(1,3) (2,1)-(3,1)	6	0.28012
(0,1)-(1,0) (0,3)-(1,3) (3,0)-(3,1)	3	0.28079
(0,1)-(0,2) (1,0)-(2,0) (0,2)-(0,3) (2,0)-(3,0) (1,3)-(2,2) (2,2)-(3,1)	6	0.28397
(0,2)-(1,1) (1,1)-(2,0) (0,2)-(1,2) (2,0)-(2,1) (1,2)-(2,2) (2,1)-(2,2)	6	0.29756
(1,1)-(1,2) (1,1)-(2,1) (1,2)-(2,1)	3	0.30902

Subface Definition

Vertices	Direction Coefficients
	A	B	C
(0,0) (0,1) (1,0)	0.00856	0	0.05426
(0,1) (0,2) (1,1)	0.0264	-0.01112	0.06529
(0,1) (1,0) (1,1)	-0.01963	0	-0.06517
(0,2) (0,3) (1,2)	0.04098	-0.02172	0.05414
(0,2) (1,1) (1,2)	-0.04131	0.01224	-0.06572
(0,3) (0,4) (1,3)	0.03971	-0.02264	0.03046
(0,3) (1,2) (1,3)	-0.04819	0.02075	-0.04335
(1,0) (1,1) (2,0)	0.0264	0.01112	0.06529
(1,1) (1,2) (2,1)	0.0502	0	0.06572
(1,1) (2,0) (2,1)	-0.04131	-0.01224	-0.06572
(1,2) (1,3) (2,2)	0.05629	-0.0106	0.04245
(1,2) (2,1) (2,2)	-0.05815	0	-0.05285
(2,0) (2,1) (3,0)	0.04098	0.02172	0.05414
(2,1) (2,2) (3,1)	0.05629	0.0106	0.04245
(2,1) (3,0) (3,1)	-0.04819	-0.02075	-0.04335
(3,0) (3,1) (4,0)	0.03971	0.02264	0.03046

Fastening Angles

Vertices	Edge	Fastening Angle
		radians	degrees
(0,0) (0,1) (1,0)	(0,0) (0,1)	1.47908	84.74502
	(0,1) (1,0)	1.52035	87.10942
	(1,0) (0,0)	1.47908	84.74502
(0,1) (0,2) (1,1)	(0,1) (0,2)	1.47922	84.75287
	(0,2) (1,1)	1.49233	85.50421
	(1,1) (0,1)	1.47593	84.56438
(0,1) (1,0) (1,1)	(0,1) (1,0)	1.48507	85.08838
	(1,0) (1,1)	1.48445	85.05278
	(1,1) (0,1)	1.48445	85.05278
(0,2) (0,3) (1,2)	(0,2) (0,3)	1.47922	84.75287
	(0,3) (1,2)	1.47593	84.56438
	(1,2) (0,2)	1.49233	85.50421
(0,2) (1,1) (1,2)	(0,2) (1,1)	1.47441	84.4777
	(1,1) (1,2)	1.48522	85.09681
	(1,2) (0,2)	1.47441	84.4777
(0,3) (0,4) (1,3)	(0,3) (0,4)	1.47908	84.74502
	(0,4) (1,3)	1.47908	84.74502
	(1,3) (0,3)	1.52035	87.10942
(0,3) (1,2) (1,3)	(0,3) (1,2)	1.48445	85.05278
	(1,2) (1,3)	1.48445	85.05278
	(1,3) (0,3)	1.48507	85.08838
(1,0) (1,1) (2,0)	(1,0) (1,1)	1.47593	84.56438
	(1,1) (2,0)	1.49233	85.50421
	(2,0) (1,0)	1.47922	84.75287
(1,1) (1,2) (2,1)	(1,1) (1,2)	1.47559	84.54528
	(1,2) (2,1)	1.47559	84.54528
	(2,1) (1,1)	1.47559	84.54528
(1,1) (2,0) (2,1)	(1,1) (2,0)	1.47441	84.4777
	(2,0) (2,1)	1.47441	84.4777
	(2,1) (1,1)	1.48522	85.09681
(1,2) (1,3) (2,2)	(1,2) (1,3)	1.47593	84.56438
	(1,3) (2,2)	1.47922	84.75287
	(2,2) (1,2)	1.49233	85.50421
(1,2) (2,1) (2,2)	(1,2) (2,1)	1.48522	85.09681
	(2,1) (2,2)	1.47441	84.4777
	(2,2) (1,2)	1.47441	84.4777
(2,0) (2,1) (3,0)	(2,0) (2,1)	1.49233	85.50421
	(2,1) (3,0)	1.47593	84.56438
	(3,0) (2,0)	1.47922	84.75287
(2,1) (2,2) (3,1)	(2,1) (2,2)	1.49233	85.50421
	(2,2) (3,1)	1.47922	84.75287
	(3,1) (2,1)	1.47593	84.56438
(2,1) (3,0) (3,1)	(2,1) (3,0)	1.48445	85.05278
	(3,0) (3,1)	1.48507	85.08838
	(3,1) (2,1)	1.48445	85.05278
(3,0) (3,1) (4,0)	(3,0) (3,1)	1.52035	87.10942
	(3,1) (4,0)	1.47908	84.74502
	(4,0) (3,0)	1.47908	84.74502