Also known as "vector equilibrium". Here are some descriptions..

Whereas a cube is 6 squares touching each other on the edges, this is 6 squares touching each other at the corners.

Whereas an octahedron is 8 triangles touching each other on the edges, this is 8 triangles touching each other at the corners.

This is a cube with the corners chopped off.

This is an octahedron with the corners chopped off.

This is 4 hexagons evenly spaced as great circles in a sphere.

Since it is not naturally rigid, my toothpic'n'raisin model has a central raisin with radiating toothpics. This makes it really rigid, being then composed of a 3d matrix of tetrahedra. It is actually part of a space filling pattern called "octet truss", very often used in modern architecture for making very rigid roofs, beams, bridges, and so on.