21 Class II Method 1 Icosahedral Coordinates

1Two tables give Class II Method 1 information for the’icosa breakdown of frequencies $12, 8, 6, 4, 2$ . (The reader will remember that all Class II frequencies are even.)

2 The unit of attention is not the icosa face but its Class II tri- angle (see Chapter 10). Five of these triangles are covered in the tables: see Diagram 12.5 and the explanation in Chapter 12. Ellipsoidal structures can thus be computed as far down as an equatorial truncation plane. For spheres we disregard most of the data provided and use only the left half of the top Class II triangle (Diagram 12.4); this would be, for example, the area bounded by 0,0; 4,0; 4,2 in the $8 v$ case shown in Diagram 12.5.

3 An HP-65 program using Equations 12.4, 12.5, 12.6, 12.7, 12.9 generated the Class II triangle data; a second program then obtained the remaining four triangles by successive rotations using Equations 14.1 and 14.2.





46 vi	512v		6e
70,0	80,0	900.0000000	1000.0000000
	111,0	1200.0000000	135.5165213
	141,1	1572.0000000	165.5165213
171,0	182,0	1900.0000000	2011.4729759
	212,1	2236.0000000	239.3247035
241,1	252,2	2672.0000000	2711.4729759
	283,0	2900.0000000	3017.7818206
	313,1	3222.3861776	3314.9473413
	343,2	3549.6138225	3614.9473413
	373,3	3872.0000000	3917.7818206
402,0	414,0	4200.0000000	4324.3119302
	444,1	4516.0353713	4621.2489135
472,1	484,2	4936.0000000	5020.0767513
	514,3	5255.9646288	5321.2489135
542,2	554,4	5672.0000000	5724.3119302
	585,0	5900.0000000	6030.9008742
	615,1	6212.4463843	6327.8434843
	645,2	6527.7323015	6626.0719770
	675,3	6844.2676986	6926.0719770
	705,4	7159-5536157	7227.8434843
	735,5	7472.0000000	7530.9008742
763,0	776,0	7800.0000000	7937.3773681
	806,1	8110.1562304	8234.4779740
833,1	846,2	8522.3861776	8632.4522840
	876,3	8836.0000000	8931.7174744
903,2	916,4	9249.6138225	9332.4522840
	946,5	9561.8437696	9634.4779740
973,3	986,6	9972.0000000	10037-3773681
	1017,0	10200.0000000	10343.9961269
	1047,1	1058.5725404	10640.9443707
	1077,2	10818.7046980	10938.8872075
	1107,3	11130.0743861	11237.7470129
	1137,4	11441.9256139	11537.7470129
	1167,5	11753.2953020	11838.8872076
	1197,6	12063.4274595	12140.9443707
1224,0	1238,0	12400.0000000	12551.0265527
	1268,1	1277.8176058	12847.7365997
	1298,2	13016.0353713	13145.1328359
	1328,3	13325.7052785	13443.8225702
1354,2	1368,4	13736.0000000	13843.3581976
	1398,5	14046.2947215	14143.8225702
1424,3	1438,6	14455.9646287	14545.1328359





1466v 12v	147V	1489
1499,0	15000.0000000	15158.2825256
1529,1	1537.1842330	15454.8527896
1559,2	15614.7278968	15751.9590943
1589,3	15922.3861776	16049.6967416
1619,4	16231.3846950	16348.9816797
1649,5	16540.6153050	16648.9816797
1679,6	16849.6138224	16949.6967416
1705,0 10,0	17100.0000000	17265.5384985
17310,1	1746.6453720	17562.0852025
1765,1 10,2	17713.6138224	17859.0080313
17910,3	18020.7140829	18156.4260598
1825,2 10,4	18327.7323015	18454.3940654
18510,5	18636.0000000	18754.1102454
1885,3 10,6	18944.2676985	19054.3940654
19111,0	19200.0000000	19375.5689243
19411,1	1956.1814143	19669.2059650
19711,2	19812.6538762	19966.0652074
20011,3	20119.2655182	20263.2739586
20311,4	20425.8437697	20560.9162276
20611,5	20732.2211414	20859.0222838
20911,6	21039.7788586	21159.0222838
2126,0 12,0	21300.0000000	21479.1876831
21512,1	2165.7778072	21776.0076786
2186,1 12,2	21911.8185859	22072.9167205
22112,3	22218.0000000	22370.0353713
2246,2 12,4	22524.1814143	22667.4616665
22712,5	22830.2221929	22965.2555423
2306,3 12,6	23136.0000000	23263.4349488
23313,0	23400.0000000	23585.6641771
23613,1	2375.7778072	23882.5457713
23913,2	24011.8185859	24179.4116562
24213,3	24318.0000000	24476.3861775
24513,4	24624.1814143	24773.5844349
24813,5	24930.2221929	25071.0914502
25113,6	25236.0000000	25368.9514701
2547,0 14,0	25500.0000000	25692.2531211
25714,1	2585.7778072	25989.2841783
2607,1 14,2	26111.8185857	26286.1926965
26314,3	26418.0000000	26583.0956449
2667,2 14,4	26724.1814143	26880.1168545
26914,5	27030.2221929	27177.3633902
2727,3 14,6	27336.0000000	27474.9079247
	(Continued)





2756v 12v	276V	277e
27815,0 27915,1 28015,2 28115,3 28215,4 28315,5 28415,6	28500.0000000 2865.7778072 28711.8185857 28818.0000000 28924.1814143 29030.2221929 29136.0000000	29298.7832307 29396.0423546 29493.0817398 29590.0000000 29686.9182604 29783.9576455 29881.2167695
2998,0 16,0 30016,1 3018,1 16,2 30216,3 3038,2 16,4 30416,5 3058,3 16,6	30600.0000000 3075.7778072 30811.8185858 30918.0000000 31024.1814143 31130.2221929 31236.0000000	313105.0920754 314102.6366099 31599.8831455 31696.9043551 31793.8073037 31890.7158218 31987.7468790





3206v 12v	321V	322e
32317,0	32400.0000000	325111.0485300
32617,1	3275.7778072	328108.9085499
32917,2	33011.8185857	331106.4155651
33217,3	33318.0000000	334103.6138226
33517,4	33624.1814143	337100.5883439
33817,5	33930.2221929	34097.4542289
34117,6	34236.0000000	34394.3358230
3449,0 18,0	34500.0000000	346116.5650512
34718,1	3485.7778072	349114.7444578
3509,1 18,2	35111.8185857	352112.5383336
35318,3	35418.0000000	355109.9646288
3569,2 18,4	35724.1814143	358107.0832796
35918,5	36030.2221929	361103.9923215
3629,3 18,6	36336.0000000	364100.8123170





3652\> 4m 8m	3664>	367e
368o 369o 370o 371o 372 $a$ 373o	37400.0000000	37500.0000000
376 3771,0	37800.0000000	3798.4441473
380 3811,1	38272.0000000	3838,4441473
3841,0 2,0	38500.0000000	38617.7818206
387 3882,1	38936.0000000	39014.5454366
3911,1 2,2	39272.0000000	39317.7818206
394 3953,0	39600.0000000	39727.6098530
398 3993,1	40022.3861776	40123.5260254
402 4033,2	40449.6138225	40523.5260254
406 4073,3	40872.0000000	40927.6098530
410o 411■=r 412o 413CXJ 414o	41500.0000000	41637.3773681
417 4184,1	41916.0353712	42033.3269362
4212,1 4,2	42236.0000000	42331.7174744
424 4254,3	42655.9646288	42733.3269362
4281,1 2,2 4,4	42972.0000000	43037.3773681
431 4325,0	43300.0000000	43447.4702086
435 4365,1	43712.4463844	43842.9758510
439 4405,2	44127.7323014	44240.7965529
443 4445,3	44544.2676986	44640.7965529
447 4485,4	44959.5536157	45042.9758510
4513,0 6,0	45200.0000000	45358.2825256
454 4556,1	45610.9252950	45753.3310985
4583,1 6,2	45922.3861776	46049.6967416
461 4626,3	46336.0000000	46448.8895123
4653,2 6,4	46649.6138224	46749.6967416





4682m 4m 8m	469V	470e
471 4727,0 4737,1 4747,2 4757,3 4767,4	47700.0000000 4789.7323015 47919.9646288 48030.0743861 48141.9256139	48269.0948426 48364.0653713 48459.8480232 48556.7273505 48656.7273505
4870 H cxj cnr 488oo00 coco co 489O rd (XI 490-=r -=r 491O rd 492A 493CXJ CXJ	494.00.0000000 4958.7723551 49618.0000000 49727.2276449 49836.0000000	49979.1876831 50074.4432523 50170.0353712 50266.3105890 50363.4349488
504 5059,0 5069,1 5079,2 5089,3 5099,4	51000.0000000 5118.7723551 51218.0000000 51327.2276449 51436.0000000	51588.9551982 51684.3401063 51779.7052785 51875.4545635 51971.8790961
5205,0 10.0 521 52210,1 5235,1 10,2 524 52510,3 5265,2 10,4	52700.0000000 5288.7723551 52918.0000000 53027.2276449 53136.0000000	53298.7832307 53394.5840965 53490.0000000 53585.4159036 53681.2167695
537 53811,0 53911,1 54011,2 54111,3 54211,4	54300.0000000 5448.7723551 54518.0000000 54627.2276449 54736.0000000	548108.1209040 549104.5454366 550100.2947216 55195.6598938 55291.0448019
5533,0 6,0 12,0 554 55512,1 5566,1.12,2 557 5581? ? 5593,1 6,2 12*4	56000.0000000 5618.7723551 56218.0000000 56327.2276449 56436.0000000	565116.5650512 566113.6894110 567109.9646288 568105.5567478 569100.8123170