< Waterman's Polyhedral mensuration chart by Steve Waterman June 2010

Waterman's Polyhedral Mensuration chart

compilation by Steve Waterman June 2010

All Polyhedron Volumes = the shortest edge3 times below values.

equal edged polyhedron containing RHOMBUS

Special thanks to Jim McNeil [ data is shown in bold ] and Roger Kaufman for creating all their related rhombus material.

and to Rob Webb the creator of Great Stella , which allowed extrapolations to deteremine the values below.

Edge values in blue correspond to a poly having the volume (as seen one column over to the right )
...should the Short Face Diagonal be assigned a value of 1, instead of to the shortest edge.


RHOMBIC DODECAHEDRON             SFD = short face diagonal      LFD =  long face diagonal

 
name
SFD
volume
LFD
S2+ L2
Rhombic dodecahedron
1.154700
3.079201435678
1.632993
4

REDUCED RHOMBIC TRIACONTAHEDRON

 
name
SFD
volume
LFD
S2+ L2
Reduced RTC
1.514622
6.15536707435054
1.701302
5.188508
   
1
5.29508497187478
Φ
Φ + 2
Twice Reduced RTC 
1.514622
2.46214682974021
1.701302
5.188508
   
1
2.11803398874991
Φ
Φ + 2

ONE FORM OF RHOMBUS PRESENT

 
name
SFD
volume edge 1
LFD
S2+ L2
Rhombic Triacontahedron
1.514622
12.310734148701
1.701302
5.188508
   
1
10.5901699437495
Φ
Φ + 2
Expanded Rhombic
1.514622
115.727921007578
1.701302
5.188508
 
      Triacontahedron
1
99.5536363553422
Φ
Φ + 2
'Snub' Rhombic
1.405502
103.925880362897
1.705584
4.884453
 
      Triacontahedron
1
91.200318609996
√(8/3)
8/3
Rhombi-propello-icosahedron
1.091322
46.1947684296956
1.676012
4
   
1
35.5413931805438
1.535764
3.358571
'Faceted' Rhombic
0.894427
54.2397041007472
1.788854
4
 
      Enneacontahedron
1
75.8022909054648
2
5
Rhombified Goldberg
1.014485
91.047597471245
1.723607
4
 
      Fullerene C80
1
87.2030614838073
1.6989970
2.88659
Rhombified Petrie Faceted
1.014485
339.901304023734
1.723607
4
 
      Trnncated Dodecahedron
1
325.548780379062
1.6989970
2.88659
Rhombified Face Faceted
0.820972
88.9710566278793
1.823734
4
      
      Trnncated Dodecahedron
1
160.79179312671
2.221433
4.934765

2 FORMS OF RHOMBI PRESENT

 
name
SFD
volume
LFD S2+ L2
Rhombic Enneacontahedron
0.713644
61.3695311951403
1.868345
4
   
1
168.852549156229
Φ + 1
Φ + 2
   
Φ
168.852549156229
2.288246
7.854103
Rhomibfied Stellated Snub
1.165330
119.246976993682
1.625425
4
        Rhombic Triacontahedron
1
86.0407341901257
1.623428
2.635518
   
1.114930
86.0407341901257
1.660400
4

3 FORMS OF RHOMBI PRESENT

 
name
SFD
volume edge 1
LFD S2+ L2
Rhombified Face Faceted
0.825984
209.88576104309
1.821469
4
        Truncated Icosidodecahedron
1
372.450226365985
2.205212
5.862960
   
1.213313
372.450226365985
2.09543
5.862955
   
1.455724
372.450226365985
1.93490
5.862970
Rhombified Face Faceted Petrie
0.832019
338.943488456521
1.818721
4
         Expanded Truncated
1
588.475257544304
2.185913
4.778216
              Dodecahedron
1.217938
588.475257544304
2.072401
6.261589
   
1.437919
588.475257544304
1.926293
6.362457
Rhombified Face Faceted
0.811393
213.021194294216
1.828016
4
        Goldberg Fullerene C140
1
398.775472784875
2.252934
6.075712
   
1.051462
398.775472784875
1.701302
4
   
1.295872
398.775472784875
2.096765
6.075708
Tetra-linear rhombus
1.008038
245.471531101742
1.727385
4
   
1
239.646281362876
1.713612
3.936466
   
1.120767
239.646281362876
1.637176
3.936464
   
1.187530
239.646281362876
1.589414
3.936464

Historical algorithm for SFD2 + SLD2 = [4]

plus these exceptions ( 5.188508, 4.884453 )

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