Two views follow:
Therefore these figures are true to the original. Obviously the name cuboctahedron is formed by the words cube and octahedron.
The cuboctahedron belongs to the 13 Archimedean solids. I made a page (in German only). Those who know how to use the 3D-View, can see the cuboctahedron threedimensionally. You can recognize that the cuboctahedron can develop from a (green)
cube. You connect the centres of the cube edges. Thus eight pyramids arise,
which you must cut off. The remaining solid is the cuboctahedron.
Derivations Area If a is the length of the edge of the cuboctahedron, the surface ist O=6*a²+8*(1/4)sqrt(3)a²=[6+2sqrt(3)]a². You use the area formulas A=(1/4)sqrt(3)a² of the equilateral triangle and A=a² of the square. Volume The producing cube has the edge length sqrt(2)a. Subtract the volumes of the eight triangle pyramids from the volume of the producing cube. Volume of the pyramid
Thickness Two squares lie in opposite to each other. Their distance is d _{1}=sqrt(2)a.
Two triangles lie in opposite to each other.
Circumscribed sphere R
Inscribed sphere There is no inscribed sphere. It has to touch all squares and triangles. But the distances are different.
Hexagons There are pairs of triangles at the cuboctahedron. In the middle planes there are regular hexagons as borders. There are four different hexagons.
Closest packing of spheres If you lay around one (red) sphere six equal spheres and lay in the dips three more spheres above and below, then the centres of the (grey) spheres are the corners of a cuboctahedron. In 2D six circles touch a central circle. 24 hyperspheres touch a central hyperspheres in the fourdimensional case. Numbers like 6,12,24 are called "kissing numbers". Euler's path Four edges meet at the corners of the cuboctahedron. Therefore it is possible to follow the edges, so that you use the edges once only. You find more on my page House of Santa Claus.
You see:
There is a template in the book (1) "M.C.Escher Kaleidozyklen".
English Eric W. Weisstein (MathWorld)
Eric Swab
George W. Hart
Gijs Korthals Altes
H. B. Meyer (Polyhedra plaited with paper strips)
Jaap Scherphuis
Kenneth James Michael MacLean
Poly
Ulrich Reitebuch
Wikipedia
German Claus Michael Ringel
Geneviève Tulloue ( Figures Animées pour la Physique )
H. B. Meyer (Polyeder aus Flechtstreifen)
Horst Steibl
Natalie Wood, Christoph Pöppe
Wikipedia
Feedback: Email address on my main page
This page is also available in German. URL of
my Homepage:
© 2004 Jürgen Köller |
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