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Euclid's Construction of a Regular Dodecahedron (XIII.17)
Let
and
be the centers of the two adjacent cube faces
and
with common side
, and let
,
,
, and
be the midpoints of
,
,
, and
.
,
, and
are points that satisfy the golden section conditions
,
, and
.
and
are perpendicular to
,
is perpendicular to
, and
.
is one face of a regular dodecahedron.
The other faces are constructed in the same way.
Contributed by:
Milana Dabic
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For more information, see
http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII17.html
.
RELATED LINKS
Dodecahedron
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Euclid's Construction of a Regular Dodecahedron (XIII.17)
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/EuclidsConstructionOfARegularDodecahedronXIII17/
Contributed by:
Milana Dabic
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