On all fours, means on hands and knees.
But, I don't know what 'on all four corners' means unless it is referring to the four corners of a table or bureau.
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Points and corners are all vertices!
No. A circle has no corners and a square has four corners. There is no object that has no corners and four corners.
"Vertices" means corners. "Tetra" means four and "hedron" means side, so a tetrahedron is a four sided object. A tetrahedron looks like pyramid. Each side is a triangle. The bottom of a tetrahedron is a triangle, and a tetrahedron goes up to a point at the top. The three corners of the triangle at the bottom plus the point at the top gives you a total of four corners.
four sides and four corners
rectangle