File:4 concentric Platonic solids and 6 named points.svg

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Captions

Captions

Designated by six letters,  the face centers of a cube are the vertices of a regular octahedron,  which is the intersection of the two regular tetrahedra of same vertices as the cube,  and same center as the other pair of dual polyhedra.

Summary

[edit]
Description
English:
Designated by six letters,  the face centers of a cube are the vertices
of a regular octahedron,  which is the intersection of the two regular tetrahedra
of same vertices as the cube,  and same center as the other pair of dual polyhedra.

The  twelve  edges  of  the  dual  tetrahedra  intersect  pairwise  perpendicularly
at  their  midpoint,    like   elsewhere   the   twenty‑four   edges   of   another   pair
cube‑octahedron.   Here  on  the  present  page,   the  pair  cube‑octahedron  has
also  its  twenty‑four  edges  pairwise  perpendicular,   but  without  common  midpoint.

Français :
Désignés  par  six  lettres,   les  centres  des  faces  d’un  cube  sont  les  sommets
d’un octaèdre régulier,  qui est l’intersection des deux tétraèdres réguliers de mêmes
sommets  que  le  cube,   et  de  même  centre  que  l’autre paire de polyèdres duaux.

Les  douze  arêtes  de  ces  tétraèdres  duaux  se  coupent  deux  à  deux  perpendiculairement
en  leur  milieu,   comme  ailleurs  les  vingt‑quatre  arêtes  d’une  autre  paire  cube‑octaèdre.
Dans  cette  page‑ci,   la  paire  cube‑octaèdre  a  aussi  ses  vingt‑quatre  arêtes
deux  à  deux  perpendiculaires,   mais  sans  milieu  commun.
Date
Source Own work
Author Arthur Baelde
Other versions
With  a  visible  cube
Without  visible  cube
Four   concentric   Platonic   solids
including  a  cube  and  its  dual
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Licensing

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Arthur Baelde, the copyright holder of this work, hereby publishes it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
Attribution: Arthur Baelde
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Under the following conditions:
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  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current10:35, 6 October 2024Thumbnail for version as of 10:35, 6 October 2024650 × 600 (2 KB)Arthur Baelde (talk | contribs) with two small discs that mark points 
12:59, 5 October 2024Thumbnail for version as of 12:59, 5 October 2024650 × 600 (2 KB)Arthur Baelde (talk | contribs)Uploaded own work with UploadWizard

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