In geometry, the Reeve tetrahedra are a family of polyhedra with vertices at ( 0 , 0 , 0 ) , ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 1 , 1 , r ) , {\displaystyle {\begin{array}{lcl}(0,&0,&0),\\(1,&0,&0),\\(0,&1,&0),\\(1,&1,&r),\end{array}}} where r is a positive integer. They are named after John Reeve, who in 1957 used them to show that higher-dimensional generalizations of Pick's theorem do not exist.
In geometry, the Reeve tetrahedra are a family of polyhedra with vertices at ( 0 , 0 , 0 ) , ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 1 , 1 , r ) , {\displaystyle {\begin{array}{lcl}(0,&0,&0),\\(1,&0,&0),\\(0,&1,&0),\\(1,&1,&r),\end{array}}} where r is a positive integer. They are named after John Reeve, who in 1957 used them to show that higher-dimensional generalizations of Pick's theorem do not exist.
Source: Wikipedia "Reeve tetrahedra" · CC BY-SA 4.0
Share this article: X · Bluesky