09. Pentagrammic Concave Trapezohedron – 21. Star Dipyramids Trapezohedra Paperweight and emblem - Geometric Paperweight - Sacred Geometry emblem for Home Decoration

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Title: 21. Star Dipyramids Trapezohedra Paperweight and emblem - Geometric Paperweight - Sacred Geometry emblem for Home Decoration Model Size: 3 in Series: Geometry Family List: 01. Heptagrammic Concave Trapezohedron 02. Heptagrammic Dipyramid Pattern 1 03. Heptagrammic Dipyramid Pattern 2 04. Heptagrammic Trapezohedron Pattern 1 05. Heptagrammic Trapezohedron Pattern 2 07. Ocatgrammic Dipyramid 08. Octagrammic Trapezohedron 09. Pentagrammic Concave Trapezohedron 10. Pentagrammic Dipyramid 11. Pentagrammic Trapezohedron Star Dipyramids and Trapezohedra: Infinite Self-Intersecting Duals of Star Prisms and Antiprisms Star dipyramids and trapezohedra form infinite families of isohedral polyhedra that emerge as duals to uniform star prisms and star antiprisms, featuring self-intersecting triangular or kite-shaped faces derived from dense star polygon bases like pentagrams {5/2} or higher Schläfli symbols. These nonconvex structures preserve face-transitivity and constant dihedral angles, producing dense, interwoven patterns with higher topological density while lacking full polyhedral group symmetries (tetrahedral, octahedral, or icosahedral). Examples include the pentagrammic dipyramid (dual to the pentagrammic prism) with 10 intersecting isosceles triangles, and corresponding star trapezohedra with concave or crossing kite faces, offering a bridge between convex duals and extreme star geometry. In 3D visualizations, star dipyramids appear as elongated, penetrating triangular…