This commit is contained in:
Guilhem Lavaux 2021-06-21 16:38:20 +02:00
parent a0f0371126
commit 7f3ae182e1
76 changed files with 76901 additions and 0 deletions

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The 12 vertices of an icosohedron, kindly provided by Mathematica.
x y z
0.0000000000000000000 0.0000000000000000000 1.1755705045849462583
1.0514622242382672121 0.0000000000000000000 0.52573111211913360603
0.32491969623290632616 1.0000000000000000000 0.52573111211913360603
-0.85065080835203993218 0.61803398874989484820 0.52573111211913360603
-0.85065080835203993218 -0.61803398874989484820 0.52573111211913360603
0.32491969623290632616 -1.0000000000000000000 0.52573111211913360603
0.85065080835203993218 0.61803398874989484820 -0.52573111211913360603
-0.32491969623290632616 1.0000000000000000000 -0.52573111211913360603
-1.0514622242382672121 0.0000000000000000000 -0.52573111211913360603
-0.32491969623290632616 -1.0000000000000000000 -0.52573111211913360603
0.85065080835203993218 -0.61803398874989484820 -0.52573111211913360603
0.0000000000000000000 0.0000000000000000000 -1.1755705045849462583

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The polygons of an icosohedron projected on the sky.
There are 20 triangular faces.
This file is created from icosohedron.vrt by:
poly2poly icosohedron.vrt icosohedron.pol
20 polygons
polygon 0 ( 3 caps, 1 weight, 0.628318530717959 str):
0.0000000000000000 1.0000000000000000 0.0000000000000000 1
-0.4253254041760199 -0.3090169943749475 0.8506508083520399 1
0.9510565162951535 -0.3090169943749475 -0.0000000000000001 1
polygon 1 ( 3 caps, 1 weight, 0.628318530717959 str):
-0.9510565162951535 0.3090169943749475 0.0000000000000001 1
0.1624598481164531 -0.5000000000000000 0.8506508083520400 1
0.5877852522924732 0.8090169943749475 -0.0000000000000000 1
polygon 2 ( 3 caps, 1 weight, 0.628318530717958 str):
-0.5877852522924732 -0.8090169943749475 0.0000000000000000 1
0.5257311121191336 0.0000000000000000 0.8506508083520399 1
-0.5877852522924732 0.8090169943749475 0.0000000000000000 1
polygon 3 ( 3 caps, 1 weight, 0.628318530717959 str):
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0.1624598481164531 0.5000000000000000 0.8506508083520400 1
-0.9510565162951535 -0.3090169943749475 0.0000000000000001 1
polygon 4 ( 3 caps, 1 weight, 0.628318530717959 str):
0.9510565162951535 0.3090169943749475 -0.0000000000000001 1
-0.4253254041760199 0.3090169943749475 0.8506508083520399 1
0.0000000000000000 -1.0000000000000000 0.0000000000000000 1
polygon 5 ( 3 caps, 1 weight, 0.628318530717959 str):
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0.4253254041760199 0.3090169943749475 -0.8506508083520399 1
polygon 6 ( 3 caps, 1 weight, 0.628318530717959 str):
-0.8506508083520399 0.0000000000000001 0.5257311121191336 1
0.6881909602355869 0.4999999999999999 0.5257311121191336 1
-0.1624598481164531 0.5000000000000000 -0.8506508083520400 1
polygon 7 ( 3 caps, 1 weight, 0.628318530717958 str):
-0.2628655560595669 -0.8090169943749475 0.5257311121191336 1
-0.2628655560595667 0.8090169943749476 0.5257311121191336 1
-0.5257311121191336 0.0000000000000001 -0.8506508083520400 1
polygon 8 ( 3 caps, 1 weight, 0.628318530717959 str):
0.6881909602355869 -0.4999999999999999 0.5257311121191336 1
-0.8506508083520399 -0.0000000000000001 0.5257311121191336 1
-0.1624598481164531 -0.5000000000000000 -0.8506508083520400 1
polygon 9 ( 3 caps, 1 weight, 0.628318530717959 str):
0.6881909602355868 0.5000000000000001 0.5257311121191336 1
-0.2628655560595668 -0.8090169943749475 0.5257311121191336 1
0.4253254041760199 -0.3090169943749475 -0.8506508083520399 1
polygon 10 ( 3 caps, 1 weight, 0.628318530717958 str):
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0.5257311121191336 0.0000000000000000 0.8506508083520400 1
polygon 11 ( 3 caps, 1 weight, 0.628318530717959 str):
0.8506508083520399 -0.0000000000000001 -0.5257311121191336 1
-0.6881909602355868 0.5000000000000001 -0.5257311121191336 1
0.1624598481164532 0.5000000000000000 0.8506508083520399 1
polygon 12 ( 3 caps, 1 weight, 0.628318530717959 str):
0.2628655560595669 0.8090169943749475 -0.5257311121191336 1
-0.6881909602355869 -0.4999999999999999 -0.5257311121191336 1
-0.4253254041760199 0.3090169943749475 0.8506508083520399 1
polygon 13 ( 3 caps, 1 weight, 0.628318530717959 str):
-0.6881909602355869 0.4999999999999999 -0.5257311121191336 1
0.2628655560595669 -0.8090169943749475 -0.5257311121191336 1
-0.4253254041760199 -0.3090169943749475 0.8506508083520399 1
polygon 14 ( 3 caps, 1 weight, 0.628318530717959 str):
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polygon 15 ( 3 caps, 1 weight, 0.628318530717958 str):
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0.5877852522924731 0.8090169943749475 0.0000000000000000 1
polygon 16 ( 3 caps, 1 weight, 0.628318530717959 str):
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polygon 17 ( 3 caps, 1 weight, 0.628318530717959 str):
0.0000000000000001 1.0000000000000000 0.0000000000000000 1
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polygon 18 ( 3 caps, 1 weight, 0.628318530717959 str):
-0.9510565162951536 0.3090169943749474 -0.0000000000000001 1
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polygon 19 ( 3 caps, 1 weight, 0.628318530717959 str):
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0.9510565162951536 -0.3090169943749474 0.0000000000000001 1

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The polygons of an icosohedron projected on the sky.
There are 20 faces.
Each face is a triangle, specified by 3 vertices.
Each vertex is specified by an azimuth and elevation, in degrees.
unit d
vertices 0 3
0 90 0 26.56505117707799 72 26.56505117707799
0 90 72 26.56505117707799 144 26.56505117707799
0 90 144 26.56505117707799 -144 26.56505117707799
0 90 -144 26.56505117707799 -72 26.56505117707799
0 90 -72 26.56505117707799 0 26.56505117707799
0 26.56505117707799 36 -26.56505117707799 72 26.56505117707799
72 26.56505117707799 108 -26.56505117707799 144 26.56505117707799
144 26.56505117707799 180 -26.56505117707799 -144 26.56505117707799
-144 26.56505117707799 -108 -26.56505117707799 -72 26.56505117707799
-72 26.56505117707799 -36 -26.56505117707799 0 26.56505117707799
36 -26.56505117707799 0 26.56505117707799 -36 -26.56505117707799
108 -26.56505117707799 72 26.56505117707799 36 -26.56505117707799
180 -26.56505117707799 144 26.56505117707799 108 -26.56505117707799
-108 -26.56505117707799 -144 26.56505117707799 180 -26.56505117707799
-36 -26.56505117707799 -72 26.56505117707799 -108 -26.56505117707799
0 -90 36 -26.56505117707799 -36 -26.56505117707799
0 -90 108 -26.56505117707799 36 -26.56505117707799
0 -90 180 -26.56505117707799 108 -26.56505117707799
0 -90 -108 -26.56505117707799 180 -26.56505117707799
0 -90 -36 -26.56505117707799 -108 -26.56505117707799