Regular octahedron: Difference between revisions
Revert to redirect, again. We should seriously consider splitting octahedron into articles on the regular and general cases, but the content there on the regular case is already much better than this, so creating a new WP:CONTENTFORK is not the right way to go. Tags: New redirect Manual revert Reverted |
Octahedron has been linked in the very first line. Why should only 2 of the 5 platonic solids not have their own page? If any details is missing, it can be filled up subsequently. Tags: Removed redirect Manual revert Reverted |
||
| Line 1: | Line 1: | ||
{{Short description|Convex polyhedron with 12 regular pentagonal faces}} |
|||
| ⚫ | |||
{{infobox polyhedron |
|||
| ⚫ | |||
| image = Octahedron.jpg |
|||
| type = [[Platonic solid]] |
|||
| faces = 8 [[regular triangle]]s |
|||
| edges = 12 |
|||
| vertices = 6 |
|||
| symmetry = [[octahedral symmetry]] <math> \mathrm{O}_\mathrm{h} </math> |
|||
| angle = 109.471° |
|||
| dual = cube |
|||
| properties = [[Convex set|convex]], [[Regular polyhedron|regular]] |
|||
| dual = cube |
|||
| net = Octahedron flat.svg |
|||
}} |
|||
A '''regular octahedron''' is an [[octahedron]] composed of [[regular polygon|regular]] triangular faces, four meeting at each [[Vertex (geometry)|vertex]]. It is an example of [[Platonic solids]], described as cosmic stellation by [[Plato]] in his dialogues. The regular octahedron, as well as the other Platonic solids, has been described by mathematicians and philosophers since antiquity. |
|||
All the faces of a regular octahedron are [[equilateral triangle]]s of the same size, and exactly four triangles meet at each vertex. A regular octahedron is convex, meaning that for any two points within it, the [[line segment]] connecting them lies entirely within it. |
|||
{{R with Wikidata item|Q12557050}} |
|||
It is one of the eight convex [[deltahedron|deltahedra]] because all of the faces are [[equilateral triangles]]. It is a [[composite polyhedron]] made by attaching two [[equilateral square pyramid]]s. Its [[dual polyhedron]] is the [[cube]], and they have the same [[Point groups in three dimensions| three-dimensional symmetry groups]], the octahedral symmetry <math> \mathrm{O}_\mathrm{h} </math>.{{r|erickson}}. Its [[Schläfli symbol]] is {3,4}. |
|||
{{Authority control}} |
|||
== References == |
|||
{{reflist|refs= |
|||
<ref name=erickson>{{cite book |
|||
| last = Erickson | first = Martin |
|||
| year = 2011 |
|||
| title = Beautiful Mathematics |
|||
| publisher = [[Mathematical Association of America]] |
|||
| url = https://books.google.com/books?id=LgeP62-ZxikC&pg=PA62 |
|||
| page = 62 |
|||
| isbn = 978-1-61444-509-8 |
|||
}}</ref> |
|||
}} |
|||
Revision as of 14:08, 9 September 2024
| Regular octahedron | |
|---|---|
 | |
| Type | Platonic solid |
| Faces | 8 regular triangles |
| Edges | 12 |
| Vertices | 6 |
| Symmetry group | octahedral symmetry |
| Dihedral angle (degrees) | 109.471° |
| Dual polyhedron | cube |
| Properties | convex, regular |
| Net | |
 | |
A regular octahedron is an octahedron composed of regular triangular faces, four meeting at each vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues. The regular octahedron, as well as the other Platonic solids, has been described by mathematicians and philosophers since antiquity.
All the faces of a regular octahedron are equilateral triangles of the same size, and exactly four triangles meet at each vertex. A regular octahedron is convex, meaning that for any two points within it, the line segment connecting them lies entirely within it.
It is one of the eight convex deltahedra because all of the faces are equilateral triangles. It is a composite polyhedron made by attaching two equilateral square pyramids. Its dual polyhedron is the cube, and they have the same three-dimensional symmetry groups, the octahedral symmetry .[1]. Its Schläfli symbol is {3,4}.
References
- ^ Erickson, Martin (2011). Beautiful Mathematics. Mathematical Association of America. p. 62. ISBN 978-1-61444-509-8.