Half icosahedron, dissection, Platonic Solids

#####Half icosahedron, dissection

I got a challenge from two children (3rd and 4th graders). They made two congruent solids using some snap triangles (polydrons, see figures). They thought it should be half a regular icosahedron but *could not put them together to make one*. Is it really half a regular icosahedron?

No. They are close but not half an icosahedron in terms of the 3D solid. But the surface is indeed true. The dihedral angle of a regular tetrahedron is about 70.53 degrees;