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<p>The problem of volume maximization for hyperbolic ideal polyhedra is studied. Each ideal polyhedron derived from a Euclidean convex uniform polyhedron or a Johnson solid <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(J_i\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1\leqslant i \leqslant 83\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>⩽</mo> <mi>i</mi> <mo>⩽</mo> <mn>83</mn> </mrow> </math></EquationSource> </InlineEquation> uniquely maximizes volume among all ideal polyhedra of the same combinatorial type. Examples of volume-maximizing ideal polyhedra not arising from Euclidean convex uniform polyhedra or Johnson solids are also discussed. Explicit formulas and numerical values for the volumes and dihedral angles of certain ideal polyhedra are provided.</p>

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Ideal polyhedra with maximum volume

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Ren Guo

摘要

The problem of volume maximization for hyperbolic ideal polyhedra is studied. Each ideal polyhedron derived from a Euclidean convex uniform polyhedron or a Johnson solid \(J_i\) J i for \(1\leqslant i \leqslant 83\) 1 ⩽ i ⩽ 83 uniquely maximizes volume among all ideal polyhedra of the same combinatorial type. Examples of volume-maximizing ideal polyhedra not arising from Euclidean convex uniform polyhedra or Johnson solids are also discussed. Explicit formulas and numerical values for the volumes and dihedral angles of certain ideal polyhedra are provided.