WOLFRAM|DEMONSTRATIONS PROJECT

Perfect Parallelepipeds

​
parallelepiped examples
1
2
3
4
5
6
7
8
9
10
edges


u
 = 271


v
 = 106

w
 = 103
minor face diagonals


v
-
w
 = 101

w
-

u
 = 266


u
-

v
 = 255
major face diagonals


v
+
w
 = 183

w
+

u
 = 312


u
+

v
 = 323
body diagonals
-

u
+

v
+
w
 = 272


u
-

v
+
w
 = 278


u
+

v
-
w
 = 300


u
+

v
+
w
 = 374
vectors:

u
= {271,0,0}

v
= 
9826
271
,
60
202398
271
,0
w
= 
6647
271
,
143754
42
4819
271
,66
8358
4819

A perfect parallelepiped is a parallelepiped with integer length edges, face diagonals, and body diagonals. In 2009 it was shown that perfect parallelepipeds exist. This Demonstration gives 10 examples together with their generating vectors and required lengths.