Solid geometry problem

First of all, the photography O of the bottom P is the vertical center of the triangle ABC (because the three sides are perpendicular to each other, there is a triple perpendicular theorem) and all three sides are equal to 1, so O is also the outer center of the triangle ABC, so the outer center of the triangle ABC coincides with the vertical center, so the triangle ABC is a regular triangle and AB=AC=BC= root number 2 is in the isosceles right triangle PAB, so the square root of OA = 6/3 is in.