Geometric Realizations of the Abstract Platonic Polyhedra
The abstract Platonic polyhedra are the abstract regular 3-polytopes whose automorphism groups are the string C-groups of rank 3 arising from the finite irreducible Coxeter groups A3, B3, and H3. The objective of this work is to construct geometric realizations of these abstract polyhedra in the Euc...
Saved in:
| Main Author: | |
|---|---|
| Format: | text |
| Published: |
Archīum Ateneo
2024
|
| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/250 https://doi.org/10.1063/5.0192096 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Ateneo De Manila University |
| id |
ph-ateneo-arc.mathematics-faculty-pubs-1251 |
|---|---|
| record_format |
eprints |
| spelling |
ph-ateneo-arc.mathematics-faculty-pubs-12512024-04-15T07:38:18Z Geometric Realizations of the Abstract Platonic Polyhedra Loyola, Mark The abstract Platonic polyhedra are the abstract regular 3-polytopes whose automorphism groups are the string C-groups of rank 3 arising from the finite irreducible Coxeter groups A3, B3, and H3. The objective of this work is to construct geometric realizations of these abstract polyhedra in the Euclidean space E3. The construction employs the algebraic version of the method of Wythoff construction which uses the faithful irreducible orthogonal representations of degree 3 of these Coxeter groups. 2024-03-07T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/250 https://doi.org/10.1063/5.0192096 Mathematics Faculty Publications Archīum Ateneo Geometry and Topology Mathematics Physical Sciences and Mathematics |
| institution |
Ateneo De Manila University |
| building |
Ateneo De Manila University Library |
| continent |
Asia |
| country |
Philippines Philippines |
| content_provider |
Ateneo De Manila University Library |
| collection |
archium.Ateneo Institutional Repository |
| topic |
Geometry and Topology Mathematics Physical Sciences and Mathematics |
| spellingShingle |
Geometry and Topology Mathematics Physical Sciences and Mathematics Loyola, Mark Geometric Realizations of the Abstract Platonic Polyhedra |
| description |
The abstract Platonic polyhedra are the abstract regular 3-polytopes whose automorphism groups are the string C-groups of rank 3 arising from the finite irreducible Coxeter groups A3, B3, and H3. The objective of this work is to construct geometric realizations of these abstract polyhedra in the Euclidean space E3. The construction employs the algebraic version of the method of Wythoff construction which uses the faithful irreducible orthogonal representations of degree 3 of these Coxeter groups. |
| format |
text |
| author |
Loyola, Mark |
| author_facet |
Loyola, Mark |
| author_sort |
Loyola, Mark |
| title |
Geometric Realizations of the Abstract Platonic Polyhedra |
| title_short |
Geometric Realizations of the Abstract Platonic Polyhedra |
| title_full |
Geometric Realizations of the Abstract Platonic Polyhedra |
| title_fullStr |
Geometric Realizations of the Abstract Platonic Polyhedra |
| title_full_unstemmed |
Geometric Realizations of the Abstract Platonic Polyhedra |
| title_sort |
geometric realizations of the abstract platonic polyhedra |
| publisher |
Archīum Ateneo |
| publishDate |
2024 |
| url |
https://archium.ateneo.edu/mathematics-faculty-pubs/250 https://doi.org/10.1063/5.0192096 |
| _version_ |
1797546532549951488 |