Compound of a Cube and an Octahedron
(also known as the First Stellation of the Cuboctahedron)
This model can be made with nets that make each vertex. For instance, the octahedron vertices in the picture above are red. They could be made from 4 separate triangles glued together or could be cut using the top image that is pictured below. Score the lines that join the 4 triangles. Add tabs along the outside of the template. Bend along the scored lines, and glue. You then have the red bottomless pyramid with triangular faces and a square base that is in the picture above
Create the cube verticies in the same way using the bottom section of my template (3 isosceles right triangles). Score the cube edges, cut out each piece with tabs added to the outside, and glue.
Around each of the four red octahedron edges you will glue a yellow cube vertices.
To see the full-sized template click on this image: