Affine Equivalent Classes of Parallelohedra

In the paper the affine equivalence relation in the set of parallelohedra is studied. One proves the uniqueness theorem for a wide class of d-dimensional parallelohedra. From here it follows that for every d ( ≥ 2) the space of affine equivalent classes of d-dimensional primitive parallelohedra has...

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Bibliographic Details
Published inComputational Geometry, Graphs and Applications Vol. 7033; pp. 55 - 60
Main Authors Dolbilin, Nikolai, Itoh, Jin-ichi, Nara, Chie
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2011
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Algorithms & data structures
Combinatorial Type
Discrete mathematics
Equivalent Classis
Graphics programming
Hexagonal Prism
Rhombic Dodecahedron
Uniqueness Theorem
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ISBN9783642249822
3642249825
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-24983-9_6

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Summary:In the paper the affine equivalence relation in the set of parallelohedra is studied. One proves the uniqueness theorem for a wide class of d-dimensional parallelohedra. From here it follows that for every d ( ≥ 2) the space of affine equivalent classes of d-dimensional primitive parallelohedra has dimension d(d + 1)/2 − 1.
ISBN:9783642249822
3642249825
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-24983-9_6