The convex deltahedra are the triangular dipyramid, the pentagonal dipyramid, the siamese dodecahedron, the tri-augmented triangular prism and the gyro-elongated square dipyramid. Beside the regular pyramid, the octahedron and the regular icosahedron (all three of which are also convex deltahedra), they are the only other regular polyhedra whose faces consist only of equilateral triangles.
What differentiates the convex deltahedra from the platonic solids is with the platonic solids, the number of faces that meet at the vertices is constant (i.e. in a pyramid, at every vertex, there meets three faces, in the case of a regular icosahedron, each vertex joins 5 faces, and so on).
For this painting, I attributed color and meaning idiosyncratically. To my knowledge, there are no cases of assigning mystical meaning to these polyhedra.