origamio.com
Mio's Kusudama Gallery
© Mio Tsugawa
The basic polyhedron is the rhombicosidodecahedron (rhombicosidodecahedron) which is popular in origamio.com.
It has 12 pentagons, 20 triangles and 30 squares.
As for Neighbor is kite unit too, a triangle and a pentagon make a square.
This technique is same as Jewelry Box and Summer.