Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Rhombicuboctahedron
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
{{short description|Archimedean solid with 26 faces}} {{redirect|Expanded octahedron|the tensegrity structure|Jessen's icosahedron}} {{Infobox polyhedron | name = Rhombicuboctahedron | image = Rhombicuboctahedron.jpg | type = [[Archimedean solid|Archimedean]]<br>[[Uniform polyhedron]] | faces = 8 [[equilateral triangle]]s<br>18 [[Square (geometry)|square]]s | edges = 48 | vertices = 24 | symmetry = [[Octahedral symmetry]] <math> \mathrm{O}_\mathrm{h} </math><br>[[Pyritohedral symmetry]] <math> \mathrm{T}_\mathrm{h} </math> | schläfli = <math> r \begin{Bmatrix} 3 \\ 4 \end{Bmatrix} </math> | angle = square-to-square: 135° <br> square-to-triangle: 144.7° | vertex_figure = Polyhedron small rhombi 6-8 vertfig.svg | vertex_config = <math> 24 (3 \cdot 4^3) </math> | dual = [[Deltoidal icositetrahedron]] | net = Polyhedron small rhombi 6-8 net.svg }} In geometry, the '''rhombicuboctahedron''' is an [[Archimedean solid]] with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named by [[Johannes Kepler]] in his 1618 [[Harmonices Mundi]], being short for ''truncated cuboctahedral rhombus'', with cuboctahedral rhombus being his name for a [[rhombic dodecahedron]].<ref>{{multiref |{{harvp|Kepler|1997|p=[https://books.google.com/books?id=rEkLAAAAIAAJ&pg=PA119 119]}} |{{harvp|Cromwell|1997|p=[https://archive.org/details/polyhedra0000crom/page/83/mode/1up 83]}} }}</ref> The rhombicuboctahedron is an [[Archimedean solid]], and its [[dual polyhedron|dual]] is a [[Catalan solid]], the [[deltoidal icositetrahedron]]. The [[elongated square gyrobicupola]] is a polyhedron that is similar to a rhombicuboctahedron, but it is not an Archimedean solid because it is not [[vertex-transitive]]. The rhombicuboctahedron is found in diverse cultures in architecture, toys, the arts, and elsewhere.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)