The three regular cross sections of Platonic dodecahedron that are in red (one equilateral triangle and two hexagons of the 3D space) are not distorted by the projection onto the drawing plane, because these three cross sections are parallel to the drawing plane.
On a same drawing of dodecahedron, the cross section in green lines is congruent to the red one.
Such a Platonic solid has twenty vertices, as many as triangular cross sections formed by three diagonals of faces. The sixty edges of these twenty triangles are the edges of twelve regular star pentagons, each on a face of the solid.
The twenty hexagonal cross sections, of which the edge length is $2 Φ + 1$ within the greatest drawing of dodecahedron, have $20 × 6 = 12 × 10 = 120$ edges in total: the edges of twelve regular star decagons, each on a pentagonal face.
The Schäfli symbol of these twelve congruent star decagons is {10/3}. We can reveal properties of these nonconvex regular polygons through a tiling of convex regular pentagon by golden triangles.
(A golden triangle is an isosceles triangle of which the greatest length ratio of an edge to another is the golden ratio.)
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