# A Sixth Platonic solid?

[1] Wouldn't gluing a tetrahedron's one triangle to a another tetrahedron's triangle make a platonic solid ? See the picture to see clearly what I mean. Tetrahedron stacked one on each makes an another solid with $6$ faces, $5$ vertices and $9$ edges.

You can also work with the angles: Along any of the edges where the tetrahedrons are spliced together, there will be a planar angle of $120^\circ$, whereas the planar angles on each tetrahedron are $60^\circ$. Since these angles differ, the solid is not regular.