convex hull jpgs and wrls of convex hulls from point sets derived by stacking symmetrical polyhedra...

This author believes that every symmetrical polyhedron can be stacked upon itself to make a point set which will generate an unlimited series of derived polyhedron. Below, is some proof of concept for this conjecture. To see the 3-d version...click on their radius value. Here are the first 16 initial convex hulls generated with a point matrix related to stacking a waterman 8 3-4 fold   [ meaning the polygons bridging the 3-fold and 4-fold. ]

1    radius of   0.7637626158259731
2    radius of   0.8164965809277259
3    radius of   1.1180339887498947
4    radius of   1.1547005383792515
5    radius of   1.3844373104863459
6    radius of   1.6072751268321592
7    radius of   1.8027756377319950
8    radius of   1.8257418583505518
9    radius of   1.9790570145063184
10  radius of   2.0000000000000009
11  radius of   2.1408720964441872
12  radius of   2.2912878474779186
13  radius of   2.4494897427831779
14  radius of   2.5658007197234411
15  radius of   2.6925824035672514
16  radius of   2.8136571693556882



a w6 2-fold ALERNATED with w11 4-fold to make this point matrix and series.
1    radius of   3.1622776601683826
2    radius of   3.3166247903554029
3    radius of   3.8729833462074201
4    radius of   4.4721359549995841
5    radius of   5.0000000000000044
6    radius of   5.5677643628300268
7    radius of   5.9160797830996215
8    radius of   6.0000000000000062
9    radius of   6.3245553203367644
10  radius of   6.7082039324993756
11  radius of   7.0710678118654817
12  radius of   7.1414284285428575
13  radius of   7.4161984870956692
14  radius of   7.8102496759066611
15  radius of   8.1240384046359679
16  radius of   8.6602540378443926



a w11 2-fold series
1    radius of   3.1622776601683791
2    radius of   3.3166247903553994
3    radius of   4.0113475405291270
4    radius of   4.4924178547657556
5    radius of   4.6023709304898652
6    radius of   5.1256928578219787
7    radius of   5.5103208947969931
8    radius of   5.6003246659132468
9    radius of   6.0377599699346627
10  radius of   6.3675312755772548
11  radius of   6.8290821957539496
12  radius of   7.1223081039275931
13  radius of   7.5377836144440868
14  radius of   7.8044276477580876
15  radius of   7.8682330233090347
16  radius of   8.1853527718724450



a w5 3-fold series
1    radius of   2.2360679774997858
2    radius of   3.2145502536643140
3    radius of   3.7267799624996440
4    radius of   4.5825756949558345
5    radius of   5.1316014394468770
6    radius of   5.4670731556188983
7    radius of   5.6273143387113702
8    radius of   5.9348312715882763
9    radius of   6.0827625302982113
10  radius of   6.2271805640897915
11  radius of   6.3683243915142587
12  radius of   6.7741338109671823
13  radius of   7.2801098892805083
14  radius of   7.5203427817856401
15  radius of   7.6376261582597236
16  radius of   7.9791394690572046



a w25 3-4 fold series
1    radius of   0.58590407242956732
2    radius of   0.61084722178152562
3    radius of   0.68021067851378092
4    radius of   0.70181002659753644
5    radius of   0.78226613023156100
6    radius of   0.83755151322974242
7    radius of   0.85518611049413573
8    radius of   0.90603284840454767
9    radius of   0.92235907793912608
10  radius of   0.96968990273318056
11  radius of   1.04381619014363270
12  radius of   1.09952499920674600
13  radius of   1.13952071621650000
14  radius of   1.15254423297122190
15  radius of   1.19076044936048820
16  radius of   1.20322948518969080



a w6 2-fold series
1    radius of   2.2360679774997898
2    radius of   2.4494897427831783
3    radius of   2.9387690682262937
4    radius of   3.5032452487268539
5    radius of   3.6431754380934334
6    radius of   3.9886201760873288
7    radius of   4.4210241511955752
8    radius of   4.5327094044792409
9    radius of   4.8147500643146781
10  radius of   5.1786274067731339
11  radius of   5.2742944379491972
12  radius of   5.5185637130095255
13  radius of   5.8387420812114259
14  radius of   5.9237580209617882
15  radius of   6.1422530660395918
16  radius of   6.4314567839360004



1    radius of   2.6457513110645903
2    radius of   2.8284271247461898
3    radius of   3.4641016151377539
4    radius of   3.6055512754639905
5    radius of   4.1231056256176606
6    radius of   4.2426406871192883
7    radius of   4.6904157598234297
8    radius of   5.1961524227066311
9    radius of   5.7445626465380277
10  radius of   6.0827625302982185
11  radius of   6.4807406984078586
12  radius of   6.5574385243019995
13  radius of   6.8556546004010421
14  radius of   7.2111025509279765
15  radius of   7.2801098892805163
16  radius of   7.5498344352707472



a w6 2-fold MERGED with w8 3-fold series
1    radius of   2.2360679774997898
2    radius of   2.4494897427831783
3    radius of   2.6457513110645907
4    radius of   2.8284271247461903
5    radius of   2.9387690682262937
6    radius of   3.4641016151377548
7    radius of   3.5032452487268544
8    radius of   3.6055512754639905
9    radius of   3.6431754380934338
10  radius of   3.9886201760873292
11  radius of   4.1231056256176606
12  radius of   4.2426406871192883
13  radius of   4.4210241511955752
14  radius of   4.5327094044792400
15  radius of   4.6904157598234297
16  radius of   4.8147500643146781



conclusion/conjecture/algorithm

1 - A point set can be manifested by a polyhedron.
2 - That point set can be scaled into either a 1x1x1 or 2x2x2..."unit cell".
3 - The unit cell can be exploded into a larger point set.
4 - Any exploded point set can be combinded with any other exploded point set.
5 - Any combination of exploded point sets can be "serialized"...
      [ made into a unique unlimited series of polyhedron ].
6 - ANY exploded point set can be automated to generate these unlimited series of convex hulls.
       [ where each unique point distance from 0,0,0...is given a consecutive integer reference number. ]