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A disdyakis dodecahedron (DD) has 24 mirrored pairs of identical triangular faces for a total of 48.
When a DD is oriented so its corners are either on a corner or mid-edge on a P24, each face of the P24 is cut into 4 unique triangles by the edges of the DD. One of these triangles is the face of the DD itself. The remainder of each P24 face forms three distinct triangles, shown here in gray with darker colored corners.
The triangular faces of the DD are shown here in white with lighter colored corners. Its symmetries are shown as blue, yellow, and green.