Calculations for a 5-frequency Icosahedral Geodesic Patch

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

Vertices

Vertex x y z

(0,0) 0 0 0.95106

(0,1) 0.15171 -0.11022 0.93239

(1,0) 0.15171 0.11022 0.93239

(0,2) 0.32116 -0.23334 0.86424

(1,1) 0.33129 0 0.89149

(2,0) 0.32116 0.23334 0.86424

(0,3) 0.48174 -0.35001 0.74157

(1,2) 0.51365 -0.1244 0.79069

(2,1) 0.51365 0.1244 0.79069

(3,0) 0.48174 0.35001 0.74157

(0,4) 0.60683 -0.44089 0.5847

(1,3) 0.66258 -0.2407 0.63841

(2,2) 0.68487 0 0.65989

(3,1) 0.66258 0.2407 0.63841

(4,0) 0.60683 0.44089 0.5847

(0,5) 0.68819 -0.5 0.42533

(1,4) 0.75854 -0.33067 0.46881

(2,3) 0.80291 -0.11667 0.49622

(3,2) 0.80291 0.11667 0.49622

(4,1) 0.75854 0.33067 0.46881

(5,0) 0.68819 0.5 0.42533

Chord Lengths

Chords Count Length

(0,0)-(0,1) (0,0)-(1,0) (0,4)-(0,5) (0,5)-(1,4) (4,0)-(5,0) (4,1)-(5,0) 6 0.18845

(0,1)-(1,1) (1,0)-(1,1) (0,4)-(1,3) (3,1)-(4,0) (1,3)-(1,4) (3,1)-(4,1) 6 0.21464

(0,1)-(0,2) (1,0)-(2,0) (0,3)-(0,4) (3,0)-(4,0) (1,4)-(2,3) (3,2)-(4,1) 6 0.22026

(0,1)-(1,0) (0,4)-(1,4) (4,0)-(4,1) 3 0.22045

(0,2)-(1,2) (0,3)-(1,2) (2,0)-(2,1) (2,1)-(3,0) (2,2)-(2,3) (2,2)-(3,2) 6 0.23309

(0,2)-(0,3) (2,0)-(3,0) (2,3)-(3,2) 3 0.23334

(0,2)-(1,1) (1,1)-(2,0) (0,3)-(1,3) (3,0)-(3,1) (1,3)-(2,3) (3,1)-(3,2) 6 0.23514

(1,1)-(1,2) (1,1)-(2,1) (1,2)-(1,3) (1,3)-(2,2) (2,1)-(3,1) (2,2)-(3,1) 6 0.24268

(1,2)-(2,1) (1,2)-(2,2) (2,1)-(2,2) 3 0.24879

Subface Definition

Vertices Direction Coefficients

A B C

(0,0) (0,1) (1,0) 0.00412 0 0.03344

(0,1) (0,2) (1,1) 0.01255 -0.00531 0.04079

(0,1) (1,0) (1,1) -0.00902 0 -0.03959

(0,2) (0,3) (1,2) 0.02195 -0.0118 0.03995

(0,2) (1,1) (1,2) -0.02013 0.00599 -0.04381

(0,3) (0,4) (1,3) 0.02652 -0.01546 0.03011

(0,3) (1,2) (1,3) -0.02864 0.01217 -0.03731

(0,4) (0,5) (1,4) 0.02442 -0.01475 0.01793

(0,4) (1,3) (1,4) -0.02912 0.01461 -0.02423

(1,0) (1,1) (2,0) 0.01255 0.00531 0.04079

(1,1) (1,2) (2,1) 0.02508 0 0.04537

(1,1) (2,0) (2,1) -0.02013 -0.00599 -0.04381

(1,2) (1,3) (2,2) 0.03416 -0.00659 0.03844

(1,2) (2,1) (2,2) -0.03254 0 -0.0426

(1,3) (1,4) (2,3) 0.03383 -0.01016 0.02453

(1,3) (2,2) (2,3) -0.03689 0.00618 -0.03101

(2,0) (2,1) (3,0) 0.02195 0.0118 0.03995

(2,1) (2,2) (3,1) 0.03416 0.00659 0.03844

(2,1) (3,0) (3,1) -0.02864 -0.01217 -0.03731

(2,2) (2,3) (3,2) 0.03819 0 0.02754

(2,2) (3,1) (3,2) -0.03689 -0.00618 -0.03101

(3,0) (3,1) (4,0) 0.02652 0.01546 0.03011

(3,1) (3,2) (4,1) 0.03383 0.01016 0.02453

(3,1) (4,0) (4,1) -0.02912 -0.01461 -0.02423

(4,0) (4,1) (5,0) 0.02442 0.01475 0.01793

Fastening Angles

Vertices Edge Fastening Angle

radians degrees

(0,0) (0,1) (1,0) (0,0) (0,1) 1.49894 85.88288

(0,1) (1,0) 1.53195 87.77434

(1,0) (0,0) 1.49894 85.88288

(0,1) (0,2) (1,1) (0,1) (0,2) 1.4991 85.89196

(0,2) (1,1) 1.51385 86.73705

(1,1) (0,1) 1.49448 85.62737

(0,1) (1,0) (1,1) (0,1) (1,0) 1.50819 86.41266

(1,0) (1,1) 1.50278 86.10282

(1,1) (0,1) 1.50278 86.10282

(0,2) (0,3) (1,2) (0,2) (0,3) 1.49957 85.91926

(0,3) (1,2) 1.49935 85.90625

(1,2) (0,2) 1.49935 85.90625

(0,2) (1,1) (1,2) (0,2) (1,1) 1.49646 85.74076

(1,1) (1,2) 1.50359 86.14942

(1,2) (0,2) 1.49467 85.6383

(0,3) (0,4) (1,3) (0,3) (0,4) 1.4991 85.89196

(0,4) (1,3) 1.49448 85.62737

(1,3) (0,3) 1.51385 86.73705

(0,3) (1,2) (1,3) (0,3) (1,2) 1.49467 85.6383

(1,2) (1,3) 1.50359 86.14942

(1,3) (0,3) 1.49646 85.74076

(0,4) (0,5) (1,4) (0,4) (0,5) 1.49894 85.88288

(0,5) (1,4) 1.49894 85.88288

(1,4) (0,4) 1.53195 87.77434

(0,4) (1,3) (1,4) (0,4) (1,3) 1.50278 86.10282

(1,3) (1,4) 1.50278 86.10282

(1,4) (0,4) 1.50819 86.41266

(1,0) (1,1) (2,0) (1,0) (1,1) 1.49448 85.62737

(1,1) (2,0) 1.51385 86.73705

(2,0) (1,0) 1.4991 85.89196

(1,1) (1,2) (2,1) (1,1) (1,2) 1.49393 85.59562

(1,2) (2,1) 1.49962 85.92203

(2,1) (1,1) 1.49393 85.59562

(1,1) (2,0) (2,1) (1,1) (2,0) 1.49646 85.74076

(2,0) (2,1) 1.49467 85.6383

(2,1) (1,1) 1.50359 86.14942

(1,2) (1,3) (2,2) (1,2) (1,3) 1.49393 85.59562

(1,3) (2,2) 1.49393 85.59562

(2,2) (1,2) 1.49962 85.92203

(1,2) (2,1) (2,2) (1,2) (2,1) 1.49455 85.63148

(2,1) (2,2) 1.49455 85.63148

(2,2) (1,2) 1.49455 85.63148

(1,3) (1,4) (2,3) (1,3) (1,4) 1.49448 85.62737

(1,4) (2,3) 1.4991 85.89196

(2,3) (1,3) 1.51385 86.73705

(1,3) (2,2) (2,3) (1,3) (2,2) 1.50359 86.14942

(2,2) (2,3) 1.49467 85.6383

(2,3) (1,3) 1.49646 85.74076

(2,0) (2,1) (3,0) (2,0) (2,1) 1.49935 85.90625

(2,1) (3,0) 1.49935 85.90625

(3,0) (2,0) 1.49957 85.91926

(2,1) (2,2) (3,1) (2,1) (2,2) 1.49962 85.92203

(2,2) (3,1) 1.49393 85.59562

(3,1) (2,1) 1.49393 85.59562

(2,1) (3,0) (3,1) (2,1) (3,0) 1.49467 85.6383

(3,0) (3,1) 1.49646 85.74076

(3,1) (2,1) 1.50359 86.14942

(2,2) (2,3) (3,2) (2,2) (2,3) 1.49935 85.90625

(2,3) (3,2) 1.49957 85.91926

(3,2) (2,2) 1.49935 85.90625

(2,2) (3,1) (3,2) (2,2) (3,1) 1.50359 86.14942

(3,1) (3,2) 1.49646 85.74076

(3,2) (2,2) 1.49467 85.6383

(3,0) (3,1) (4,0) (3,0) (3,1) 1.51385 86.73705

(3,1) (4,0) 1.49448 85.62737

(4,0) (3,0) 1.4991 85.89196

(3,1) (3,2) (4,1) (3,1) (3,2) 1.51385 86.73705

(3,2) (4,1) 1.4991 85.89196

(4,1) (3,1) 1.49448 85.62737

(3,1) (4,0) (4,1) (3,1) (4,0) 1.50278 86.10282

(4,0) (4,1) 1.50819 86.41266

(4,1) (3,1) 1.50278 86.10282

(4,0) (4,1) (5,0) (4,0) (4,1) 1.53195 87.77434

(4,1) (5,0) 1.49894 85.88288

(5,0) (4,0) 1.49894 85.88288

Vertex	x	y	z
(0,0)	0	0	0.95106
(0,1)	0.15171	-0.11022	0.93239
(1,0)	0.15171	0.11022	0.93239
(0,2)	0.32116	-0.23334	0.86424
(1,1)	0.33129	0	0.89149
(2,0)	0.32116	0.23334	0.86424
(0,3)	0.48174	-0.35001	0.74157
(1,2)	0.51365	-0.1244	0.79069
(2,1)	0.51365	0.1244	0.79069
(3,0)	0.48174	0.35001	0.74157
(0,4)	0.60683	-0.44089	0.5847
(1,3)	0.66258	-0.2407	0.63841
(2,2)	0.68487	0	0.65989
(3,1)	0.66258	0.2407	0.63841
(4,0)	0.60683	0.44089	0.5847
(0,5)	0.68819	-0.5	0.42533
(1,4)	0.75854	-0.33067	0.46881
(2,3)	0.80291	-0.11667	0.49622
(3,2)	0.80291	0.11667	0.49622
(4,1)	0.75854	0.33067	0.46881
(5,0)	0.68819	0.5	0.42533

Chords	Count	Length
(0,0)-(0,1) (0,0)-(1,0) (0,4)-(0,5) (0,5)-(1,4) (4,0)-(5,0) (4,1)-(5,0)	6	0.18845
(0,1)-(1,1) (1,0)-(1,1) (0,4)-(1,3) (3,1)-(4,0) (1,3)-(1,4) (3,1)-(4,1)	6	0.21464
(0,1)-(0,2) (1,0)-(2,0) (0,3)-(0,4) (3,0)-(4,0) (1,4)-(2,3) (3,2)-(4,1)	6	0.22026
(0,1)-(1,0) (0,4)-(1,4) (4,0)-(4,1)	3	0.22045
(0,2)-(1,2) (0,3)-(1,2) (2,0)-(2,1) (2,1)-(3,0) (2,2)-(2,3) (2,2)-(3,2)	6	0.23309
(0,2)-(0,3) (2,0)-(3,0) (2,3)-(3,2)	3	0.23334
(0,2)-(1,1) (1,1)-(2,0) (0,3)-(1,3) (3,0)-(3,1) (1,3)-(2,3) (3,1)-(3,2)	6	0.23514
(1,1)-(1,2) (1,1)-(2,1) (1,2)-(1,3) (1,3)-(2,2) (2,1)-(3,1) (2,2)-(3,1)	6	0.24268
(1,2)-(2,1) (1,2)-(2,2) (2,1)-(2,2)	3	0.24879

Vertices	Direction Coefficients
Vertices	A	B	C
(0,0) (0,1) (1,0)	0.00412	0	0.03344
(0,1) (0,2) (1,1)	0.01255	-0.00531	0.04079
(0,1) (1,0) (1,1)	-0.00902	0	-0.03959
(0,2) (0,3) (1,2)	0.02195	-0.0118	0.03995
(0,2) (1,1) (1,2)	-0.02013	0.00599	-0.04381
(0,3) (0,4) (1,3)	0.02652	-0.01546	0.03011
(0,3) (1,2) (1,3)	-0.02864	0.01217	-0.03731
(0,4) (0,5) (1,4)	0.02442	-0.01475	0.01793
(0,4) (1,3) (1,4)	-0.02912	0.01461	-0.02423
(1,0) (1,1) (2,0)	0.01255	0.00531	0.04079
(1,1) (1,2) (2,1)	0.02508	0	0.04537
(1,1) (2,0) (2,1)	-0.02013	-0.00599	-0.04381
(1,2) (1,3) (2,2)	0.03416	-0.00659	0.03844
(1,2) (2,1) (2,2)	-0.03254	0	-0.0426
(1,3) (1,4) (2,3)	0.03383	-0.01016	0.02453
(1,3) (2,2) (2,3)	-0.03689	0.00618	-0.03101
(2,0) (2,1) (3,0)	0.02195	0.0118	0.03995
(2,1) (2,2) (3,1)	0.03416	0.00659	0.03844
(2,1) (3,0) (3,1)	-0.02864	-0.01217	-0.03731
(2,2) (2,3) (3,2)	0.03819	0	0.02754
(2,2) (3,1) (3,2)	-0.03689	-0.00618	-0.03101
(3,0) (3,1) (4,0)	0.02652	0.01546	0.03011
(3,1) (3,2) (4,1)	0.03383	0.01016	0.02453
(3,1) (4,0) (4,1)	-0.02912	-0.01461	-0.02423
(4,0) (4,1) (5,0)	0.02442	0.01475	0.01793

Vertices	Edge	Fastening Angle
Vertices	Edge	radians	degrees
(0,0) (0,1) (1,0)	(0,0) (0,1)	1.49894	85.88288
	(0,1) (1,0)	1.53195	87.77434
	(1,0) (0,0)	1.49894	85.88288
(0,1) (0,2) (1,1)	(0,1) (0,2)	1.4991	85.89196
	(0,2) (1,1)	1.51385	86.73705
	(1,1) (0,1)	1.49448	85.62737
(0,1) (1,0) (1,1)	(0,1) (1,0)	1.50819	86.41266
	(1,0) (1,1)	1.50278	86.10282
	(1,1) (0,1)	1.50278	86.10282
(0,2) (0,3) (1,2)	(0,2) (0,3)	1.49957	85.91926
	(0,3) (1,2)	1.49935	85.90625
	(1,2) (0,2)	1.49935	85.90625
(0,2) (1,1) (1,2)	(0,2) (1,1)	1.49646	85.74076
	(1,1) (1,2)	1.50359	86.14942
	(1,2) (0,2)	1.49467	85.6383
(0,3) (0,4) (1,3)	(0,3) (0,4)	1.4991	85.89196
	(0,4) (1,3)	1.49448	85.62737
	(1,3) (0,3)	1.51385	86.73705
(0,3) (1,2) (1,3)	(0,3) (1,2)	1.49467	85.6383
	(1,2) (1,3)	1.50359	86.14942
	(1,3) (0,3)	1.49646	85.74076
(0,4) (0,5) (1,4)	(0,4) (0,5)	1.49894	85.88288
	(0,5) (1,4)	1.49894	85.88288
	(1,4) (0,4)	1.53195	87.77434
(0,4) (1,3) (1,4)	(0,4) (1,3)	1.50278	86.10282
	(1,3) (1,4)	1.50278	86.10282
	(1,4) (0,4)	1.50819	86.41266
(1,0) (1,1) (2,0)	(1,0) (1,1)	1.49448	85.62737
	(1,1) (2,0)	1.51385	86.73705
	(2,0) (1,0)	1.4991	85.89196
(1,1) (1,2) (2,1)	(1,1) (1,2)	1.49393	85.59562
	(1,2) (2,1)	1.49962	85.92203
	(2,1) (1,1)	1.49393	85.59562
(1,1) (2,0) (2,1)	(1,1) (2,0)	1.49646	85.74076
	(2,0) (2,1)	1.49467	85.6383
	(2,1) (1,1)	1.50359	86.14942
(1,2) (1,3) (2,2)	(1,2) (1,3)	1.49393	85.59562
	(1,3) (2,2)	1.49393	85.59562
	(2,2) (1,2)	1.49962	85.92203
(1,2) (2,1) (2,2)	(1,2) (2,1)	1.49455	85.63148
	(2,1) (2,2)	1.49455	85.63148
	(2,2) (1,2)	1.49455	85.63148
(1,3) (1,4) (2,3)	(1,3) (1,4)	1.49448	85.62737
	(1,4) (2,3)	1.4991	85.89196
	(2,3) (1,3)	1.51385	86.73705
(1,3) (2,2) (2,3)	(1,3) (2,2)	1.50359	86.14942
	(2,2) (2,3)	1.49467	85.6383
	(2,3) (1,3)	1.49646	85.74076
(2,0) (2,1) (3,0)	(2,0) (2,1)	1.49935	85.90625
	(2,1) (3,0)	1.49935	85.90625
	(3,0) (2,0)	1.49957	85.91926
(2,1) (2,2) (3,1)	(2,1) (2,2)	1.49962	85.92203
	(2,2) (3,1)	1.49393	85.59562
	(3,1) (2,1)	1.49393	85.59562
(2,1) (3,0) (3,1)	(2,1) (3,0)	1.49467	85.6383
	(3,0) (3,1)	1.49646	85.74076
	(3,1) (2,1)	1.50359	86.14942
(2,2) (2,3) (3,2)	(2,2) (2,3)	1.49935	85.90625
	(2,3) (3,2)	1.49957	85.91926
	(3,2) (2,2)	1.49935	85.90625
(2,2) (3,1) (3,2)	(2,2) (3,1)	1.50359	86.14942
	(3,1) (3,2)	1.49646	85.74076
	(3,2) (2,2)	1.49467	85.6383
(3,0) (3,1) (4,0)	(3,0) (3,1)	1.51385	86.73705
	(3,1) (4,0)	1.49448	85.62737
	(4,0) (3,0)	1.4991	85.89196
(3,1) (3,2) (4,1)	(3,1) (3,2)	1.51385	86.73705
	(3,2) (4,1)	1.4991	85.89196
	(4,1) (3,1)	1.49448	85.62737
(3,1) (4,0) (4,1)	(3,1) (4,0)	1.50278	86.10282
	(4,0) (4,1)	1.50819	86.41266
	(4,1) (3,1)	1.50278	86.10282
(4,0) (4,1) (5,0)	(4,0) (4,1)	1.53195	87.77434
	(4,1) (5,0)	1.49894	85.88288
	(5,0) (4,0)	1.49894	85.88288