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Euclid's Construction of a Regular Dodecahedron (XIII.17)

step
1
2
3
4
5
construct on all cube sides
Let
P
and
Q
be the centers of the two adjacent cube faces
BEFC
and
ABCD
with common side
BC
, and let
N
,
H
,
O
, and
L
be the midpoints of
BE
,
BC
,
CF
, and
AD
.
R
,
S
, and
T
are points that satisfy the golden section conditions
PR:RN=PN:PR
,
PS:SO=PO:PS
, and
QT:TH=QH:QT
.
UR
and
VS
are perpendicular to
BEFC
,
TW
is perpendicular to
ABCD
, and
UR=VS=TW=PR=PS=PR=QT
.
UVCWB
is one face of a regular dodecahedron.
The other faces are constructed in the same way.
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