Euclid's Construction of a Regular Dodecahedron (XIII.17)
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 .
P
Q
BEFC
ABCD
BC
N
H
O
L
BE
BC
CF
AD
R
S
T
PR:RN=PN:PR
PS:SO=PO:PS
QT:TH=QH:QT
UR
VS
BEFC
TW
ABCD
UR=VS=TW=PR=PS=PR=QT
UVCWB
The other faces are constructed in the same way.