It has Oₕ octahedral symmetry.
Its collective edges represent the reflection planes of the symmetry.
It can also be seen in the corner and mid-edge triangulation of the regular cube and octahedron, and rhombic dodecahedron.

Seen in stereographic projection the edges of the disdyakis dodecahedron form 9 circles (or centrally radial lines) in the plane.
The 9 circles can be divided into two groups of 3 and 6 (drawn in purple and red), representing in two orthogonal subgroups: [2,2], and [3,3]:
It has Oₕ octahedral symmetry. Its collective edges represent the reflection planes of the symmetry. It can also be seen in the corner and mid-edge triangulation of the regular cube and octahedron, and rhombic dodecahedron.
Seen in stereographic projection the edges of the disdyakis dodecahedron form 9 circles (or centrally radial lines) in the plane. The 9 circles can be divided into two groups of 3 and 6 (drawn in purple and red), representing in two orthogonal subgroups: [2,2], and [3,3]:
Disdyakis dodecahedron