The relation of the Dodecadodecahedron to other Kepler Poinsot solids

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The Dodecadodecahedron can be considered as a kind of Archimedean Solid that arises by vertex truncation from the Great Dodecahedron or from its dual the Small Stellated Dodekahedron. Move the slider to see the transition between those objects. The Dodecadodecahedron lies in the middle between the two objects. It consists of 12 pentagons and 12 pentagon stars. They form a checker board like pattern in which they alternate while crossing an edge. Four faces (two pentagons and two stars) meet at each vertex.

The Dodecadodecahedron is a surface of genus 4 and its cell structure is exactly isomorphic to the partitioning generated by the different combinatorial types of equilateral pentagram linkages.