I modelled the cube stand I have from ziicube and modified it to fit an octahedron, any octahedron puzzle should fit, though if its really large it might become wobbly or unstable.

I used supports and a brim, the brim is probably not necessary but there is a small contact point in the middle that got separated on my first print attempt.

Since it has a square cut-out in a triangle stand it does have a front side.

I have tested with the diansheng magnetic fto and it works well, about as stable as a 3x3 on a regular cube stand.