Waterman's Polyhedral Mensuration chart
copyright by Steve Waterman June 2010

 Note: To view WRL files, download the latest version of Cortona from here
All Polyhedron Volumes = the shortest edge3 times the volume / √e values below.
 

                     LATTICE   strut lengths

             √2   √4  √6  √8  √10  √12   √14  √16   √18  √20   √22   √24   √26  √30   

  
 SYMMETRY      Td     

WATERMAN SOLIDS

truncated tetrahedron and truncated octahedron and cuboctahedron

swept from 1.5,1.5,1.5

Click on blue numbers to view rotatable polyhedron.

Conway       Dual      Geodesicized      Zonohedrified  

√
name
 C
 D
 G
Z
  
√e
   total volume  
1
  
1
1
1
1
  
√2
  
7 2/3
 
2
  
2
2
2
2
  
√2
  
7 2/3
 
3
  
3
3
3
3
  
√2
  
68 1/3
 
4
  
4
4
4
4
  
√2
  
189
  
5
  
5
5
5
5
  
√2
  
189
  
6
  
6
6
6
6
  
√2
  
280 1/3
 
7
  
7
7
7
7
  
√2
  
461 2/3
 
8
  
8
8
8
8
  
√2
  
461 2/3
 
9
  
9
9
9
    
√2
  
677
  
10
  
10
10
10
    
√2
  
810 1/3
 
11
  
11
11
11
    
√2
  
810 1/3
 
12
  
12
12
12
    
√2
  
1073 2/3
 
13
  
13
13
13
    
√2
  
1177 2/3
 
14
  
14
14
14
    
√2
  
1177 2/3
 
15
  
15
15
15
    
√2
  
1561
  
16
  
16
16
16
    
√2
  
1858 1/3
 

SYMMETRIES      

Cs Ci C2 C3 C4 C5 C6 C10 C2v C3v C4v C5v C6v C2h C3h C4h C5h C6h C10h

D2 D3 D4 D5 D6 D10 D2v D3v D4v D5v D6v D10v D2h D3h D4h D5h D6h D10h

S2 S4 S6 S10 S12 S20 T Td Th O Oh I Ih

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