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Computational geometry analysis demonstrates a novel 68-face convex polyhedron with reflection symmetry, indicating an uncatalogued structure outside established Johnson solids.
A newly discovered convex polyhedron with 48 vertices, 114 edges of unit length, and 68 regular faces (12 regular pentagons + 56 equilateral triangles). This polyhedron exhibits reflection symmetry across the Y=0 plane and is not catalogued in the Johnson solids (J1-J92, 1966-1969). Full coordinates, incidence matrix, and computational verification included.
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Librán López Marcos (2026) studied this question.
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