MathDB

Let A\equal{}A_1A_2A_3A_4 be a tetrahedron, and suppose that for each j \not\equal{} k, [A_j,A_{jk}] is a segment of length

\rho

extending from

A_j

in the direction of

A_k

. Let

p_j

be the intersection line of the planes

[A_{jk}A_{jl}A_{jm}]

and

[A_kA_lA_m]

. Show that there are infinitely many straight lines that intersect the straight lines

p_1,p_2,p_3,p_4

simultaneously.

5