If I understand the question correctly, it is a net.
tetrahedron
It's a cube.
octahedron
Octohedron, or rhomboid.
a polyhedron
An eight-face polyhedron is called an octahedron.
What polyhedron has eight sides and all of the are equilateral triangle?
pentagon
An octahedron.
tetrahedron
It's a cube.
Yes
octahedron
You're an octagon.
Octohedron, or rhomboid.
A regular octahedron.
It is a definitional requirement. If any face is not flat, then it is not a polyhedron.