Muzyka Alexander Andreevich (graduate student,
The Federal State Budget Educational Institution of Higher Education «MIREA – Russian Technological University»
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The work found all crystallographic groups of reflections in Lobachevsky spaces of dimensions 3 and 4, the fundamental polyhedra of which satisfy the following geometric conditions:
1) any two faces of the highest dimension of the fundamental polyhedron M intersect along a face of codimension one or at a point at infinity;
2) all dihedral angles of the polyhedron M are equal to 90°, 60° and 0° (the angle between faces intersecting at a point at infinity)
Polyhedra are depicted using Gram graphs. The complete list of such polyhedra contains 16 polyhedra, all of them are non-compact, all polyhedra with exception of two are pyramids.
Keywords:vertex at infinity, face, Gram’s graphs
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Read the full article …
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Citation link: Muzyka A. A. ON SOME POLYHEDRA OF FINITE VOLUME IN LOBACHEVSKY SPACE // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2024. -№09. -С. 87-95 DOI 10.37882/2223-2966.2024.9.24 |
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