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Octahedra Inscribed in a Cube*

Published online by Cambridge University Press:  03 November 2016

T. Bakos
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Extract

The following problem was proposed by Dormán Luke, Math. Gazette, Vol. XLI, p. 194 (1957):

Inscribe a regular octahedron in a cube, so that its vertices are one on each of six edges of the cube.

Four such octahedra can be inscribed; what is the solid with 32 faces which is common to these four?

Starting with the octahedron, how many cubes can we circumscribe to it in this way?

Again, what solid formed by their vertices encases them all?

Type
Research Article
Information
The Mathematical Gazette , Volume 43 , Issue 343 , February 1959 , pp. 17 - 20
Copyright
Copyright © Mathematical Association 1959

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Footnotes

*

Translated from the German by Norman W Johnson, University of Toronto.

References

* Translated from the German by Norman W Johnson, University of Toronto.