Hello, atreyyu!

Does there exist a polyhedron, whose orthogonal projections on some three planes

are a quadrilateral, a hexagon and an octagon?

Get a large potato

. . and three cookie cutters: square, hexagonal, and octagonal.

Place the potato on the table.

Use the square cutter and push it through the potato from front to back.

Use the hexagonal cutter and push it through the potato from left to right.

Use the octagonal cutter and push it through the potato from top to bottom.

The remaining potato is the desired polyhedron.