# 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.