Calculations for a 3-frequency Icosahedral Geodesic Patch

Calculations for a 3-frequency
Icosahedral Geodesic Patch
with Edge Length 1

Vertices

Vertex x y z

(0,0) 0 0 0.95106

(0,1) 0.26413 -0.1919 0.89326

(1,0) 0.26413 0.1919 0.89326

(0,2) 0.52825 -0.3838 0.69149

(1,1) 0.57735 0 0.75576

(2,0) 0.52825 0.3838 0.69149

(0,3) 0.68819 -0.5 0.42533

(1,2) 0.79238 -0.1919 0.48972

(2,1) 0.79238 0.1919 0.48972

(3,0) 0.68819 0.5 0.42533

Chord Lengths

Chords Count Length

(0,0)-(0,1) (0,0)-(1,0) (0,2)-(0,3) (0,3)-(1,2) (2,0)-(3,0) (2,1)-(3,0) 6 0.33155

(0,1)-(1,0) (0,1)-(0,2) (1,0)-(2,0) (0,2)-(1,2) (1,2)-(2,1) (2,0)-(2,1) 6 0.3838

(0,1)-(1,1) (0,2)-(1,1) (1,0)-(1,1) (1,1)-(2,0) (1,1)-(1,2) (1,1)-(2,1) 6 0.39223

Subface Definition

Vertices Direction Coefficients

A B C

(0,0) (0,1) (1,0) 0.02218 0 0.10137

(0,1) (0,2) (1,1) 0.06511 -0.02688 0.11079

(0,1) (1,0) (1,1) -0.05277 0 -0.12021

(0,2) (0,3) (1,2) 0.07452 -0.03803 0.06138

(0,2) (1,1) (1,2) -0.08977 0.02688 -0.09195

(1,0) (1,1) (2,0) 0.06511 0.02688 0.11079

(1,1) (1,2) (2,1) 0.10211 0 0.08253

(1,1) (2,0) (2,1) -0.08977 -0.02688 -0.09195

(2,0) (2,1) (3,0) 0.07452 0.03803 0.06138

Fastening Angles

Vertices Edge Fastening Angle

radians degrees

(0,0) (0,1) (1,0) (0,0) (0,1) 1.44482 82.78237

(0,1) (1,0) 1.49871 85.86993

(1,0) (0,0) 1.44482 82.78237

(0,1) (0,2) (1,1) (0,1) (0,2) 1.44463 82.77114

(0,2) (1,1) 1.4523 83.21072

(1,1) (0,1) 1.4523 83.21072

(0,1) (1,0) (1,1) (0,1) (1,0) 1.44463 82.77114

(1,0) (1,1) 1.4523 83.21072

(1,1) (0,1) 1.4523 83.21072

(0,2) (0,3) (1,2) (0,2) (0,3) 1.44482 82.78237

(0,3) (1,2) 1.44482 82.78237

(1,2) (0,2) 1.49871 85.86993

(0,2) (1,1) (1,2) (0,2) (1,1) 1.4523 83.21072

(1,1) (1,2) 1.4523 83.21072

(1,2) (0,2) 1.44463 82.77114

(1,0) (1,1) (2,0) (1,0) (1,1) 1.4523 83.21072

(1,1) (2,0) 1.4523 83.21072

(2,0) (1,0) 1.44463 82.77114

(1,1) (1,2) (2,1) (1,1) (1,2) 1.4523 83.21072

(1,2) (2,1) 1.44463 82.77114

(2,1) (1,1) 1.4523 83.21072

(1,1) (2,0) (2,1) (1,1) (2,0) 1.4523 83.21072

(2,0) (2,1) 1.44463 82.77114

(2,1) (1,1) 1.4523 83.21072

(2,0) (2,1) (3,0) (2,0) (2,1) 1.49871 85.86993

(2,1) (3,0) 1.44482 82.78237

(3,0) (2,0) 1.44482 82.78237

Vertex	x	y	z
(0,0)	0	0	0.95106
(0,1)	0.26413	-0.1919	0.89326
(1,0)	0.26413	0.1919	0.89326
(0,2)	0.52825	-0.3838	0.69149
(1,1)	0.57735	0	0.75576
(2,0)	0.52825	0.3838	0.69149
(0,3)	0.68819	-0.5	0.42533
(1,2)	0.79238	-0.1919	0.48972
(2,1)	0.79238	0.1919	0.48972
(3,0)	0.68819	0.5	0.42533

Chords	Count	Length
(0,0)-(0,1) (0,0)-(1,0) (0,2)-(0,3) (0,3)-(1,2) (2,0)-(3,0) (2,1)-(3,0)	6	0.33155
(0,1)-(1,0) (0,1)-(0,2) (1,0)-(2,0) (0,2)-(1,2) (1,2)-(2,1) (2,0)-(2,1)	6	0.3838
(0,1)-(1,1) (0,2)-(1,1) (1,0)-(1,1) (1,1)-(2,0) (1,1)-(1,2) (1,1)-(2,1)	6	0.39223

Vertices	Direction Coefficients
Vertices	A	B	C
(0,0) (0,1) (1,0)	0.02218	0	0.10137
(0,1) (0,2) (1,1)	0.06511	-0.02688	0.11079
(0,1) (1,0) (1,1)	-0.05277	0	-0.12021
(0,2) (0,3) (1,2)	0.07452	-0.03803	0.06138
(0,2) (1,1) (1,2)	-0.08977	0.02688	-0.09195
(1,0) (1,1) (2,0)	0.06511	0.02688	0.11079
(1,1) (1,2) (2,1)	0.10211	0	0.08253
(1,1) (2,0) (2,1)	-0.08977	-0.02688	-0.09195
(2,0) (2,1) (3,0)	0.07452	0.03803	0.06138

Vertices	Edge	Fastening Angle
Vertices	Edge	radians	degrees
(0,0) (0,1) (1,0)	(0,0) (0,1)	1.44482	82.78237
	(0,1) (1,0)	1.49871	85.86993
	(1,0) (0,0)	1.44482	82.78237
(0,1) (0,2) (1,1)	(0,1) (0,2)	1.44463	82.77114
	(0,2) (1,1)	1.4523	83.21072
	(1,1) (0,1)	1.4523	83.21072
(0,1) (1,0) (1,1)	(0,1) (1,0)	1.44463	82.77114
	(1,0) (1,1)	1.4523	83.21072
	(1,1) (0,1)	1.4523	83.21072
(0,2) (0,3) (1,2)	(0,2) (0,3)	1.44482	82.78237
	(0,3) (1,2)	1.44482	82.78237
	(1,2) (0,2)	1.49871	85.86993
(0,2) (1,1) (1,2)	(0,2) (1,1)	1.4523	83.21072
	(1,1) (1,2)	1.4523	83.21072
	(1,2) (0,2)	1.44463	82.77114
(1,0) (1,1) (2,0)	(1,0) (1,1)	1.4523	83.21072
	(1,1) (2,0)	1.4523	83.21072
	(2,0) (1,0)	1.44463	82.77114
(1,1) (1,2) (2,1)	(1,1) (1,2)	1.4523	83.21072
	(1,2) (2,1)	1.44463	82.77114
	(2,1) (1,1)	1.4523	83.21072
(1,1) (2,0) (2,1)	(1,1) (2,0)	1.4523	83.21072
	(2,0) (2,1)	1.44463	82.77114
	(2,1) (1,1)	1.4523	83.21072
(2,0) (2,1) (3,0)	(2,0) (2,1)	1.49871	85.86993
	(2,1) (3,0)	1.44482	82.78237
	(3,0) (2,0)	1.44482	82.78237