You can make a sphere by creating a tetrahedron (3 sided spike). Then make 19 copies and rotate them to all fit together in a central point. Sort of like segments of an orange but not.
This will make an isosahedron (20 sided polygon) which looks kind of spherical.
Probably best to use the CTRL-M method of rotation but I don't know the angles. 72 degrees probably. And some horiz/vert flipping would speed things up.
But yeah, the messy way will work too. What Zappy said.