Paper Models of Polyhedra Gijs Korthals Altes
Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia
Copyrights Š 1998-2001 Gijs.Korthals Altes All rights reserved . It's permitted to make copies for non-commercial purposes only email: gijs@korthals.altes.net
Paper Models of Polyhedra Platonic Solids Dodecahedron Cube and Tetrahedron Octahedron Icosahedron Archimedean Solids Cuboctahedron Icosidodecahedron Truncated Tetrahedron Truncated Octahedron Truncated Cube Truncated Icosahedron (soccer ball) Truncated dodecahedron Rhombicuboctahedron Truncated Cuboctahedron Rhombicosidodecahedron Truncated Icosidodecahedron Snub Cube Snub Dodecahedron Kepler-Poinsot Polyhedra Great Stellated Dodecahedron Small Stellated Dodecahedron Great Icosahedron Great Dodecahedron Other Uniform Polyhedra Tetrahemihexahedron Octahemioctahedron Cubohemioctahedron Small Rhombihexahedron Small Rhombidodecahedron S mall Dodecahemiododecahedron Small Ditrigonal Icosidodecahedron Great Dodecahedron Compounds Stella Octangula Compound of Cube and Octahedron Compound of Dodecahedron and Icosahedron Compound of Two Cubes Compound of Three Cubes Compound of Five Cubes Compound of Five Octahedra Compound of Five Tetrahedra Compound of Truncated Icosahedron and Pentakisdodecahedron
Other Polyhedra Pentagonal Hexecontahedron Pentagonalconsitetrahedron Pyramid Pentagonal Pyramid Decahedron Rhombic Dodecahedron Great Rhombihexacron Pentagonal Dipyramid Pentakisdodecahedron Small Triakisoctahedron Small Triambic Icosahedron Polyhedra Made of Isosceles Triangles Third Stellation of the Icosahedron Sixth Stellation of the Icosahedron Seventh Stellation of the Icosahedron Eighth Stellation of the Icosahedron Ninth Stellation of the Icosahedron Final Stellation of the Icosahedron Prism and Antiprism Triangular Prism Pentagonal Prism Pe ntagonal Antiprism Triangular Prism Octagonal Prism Octagonal Antiprism Pentagrammic Prism Pentagrammic Antiprism Hexagrammic Prism Hexagrammic Antiprism Twisted Rectangular Prism Kaleidocycles Hexagonal Kaleidocycle Octagonal Kaleidocycle Decagonal Kaleidocycle Other Paper Models Cylinder Tapered Cylinder Cone Special Cones "Matryoska house" "Matryoska house" 50% Globe Chevaux-de-frise
Dodecahedron
1 3 7 9.
5 12
2
10 8
11
4 6.
Dodecahedron
Dodecahedron
Cube
Tetrahedron
Cube
4 1
5
2
6
3 2
1
4
3
Tetrahedron
Octahedron
Icosahedron
Cuboctahedron
Icosidodecahedron
Truncated Tetrahedron
Truncated Octahedron
Truncated Cube
Truncated icosahedron
Truncated dodecahedron
Rhombicuboctahedron
Truncated cuboctahedron
Rombicosidodecahedron
Truncated Icosidodecahedron
Snub cube
Snub cube Right-handed
Snub dodecahedron
Snub dodecahedron Right-handed
Small Stellated Dodecahedron
On this page a model out of one piece On the next pages a model out of six pieces. Fold the long lines backwards fold the short lines forwards
1
2
3
4
5
6
8
Octahemioctahedron type 1 type 2
13
7
11
12
5
6
2
1
10
3
4
14
13
Cubohemioctahedron
Small Rhombidodecahedron (small version) Fold the dotted lines forwards Fold the other lines
Small Rhombidodecahedron (large version) Fold the dotted lines forwards Fold the other lines
A B
C
F
E
D
B
A
C
A
D
A
E
A
F
A
Small dodecahemiododecahedron
Folds the lines between the triangles forwards. Folds the other lines backwards.
Great Stellated Dodecahedron made out of one piece of paper. Cut the lines between the long and the short sides of the triangles. Fold the long lines backwards and fold the short lines forwards.
Great Stellated Dodecahedron made out of two pieces of paper. Cut the lines between the long and the short sides of the triangles. Fold the long lines backwards and fold the short lines forwards. This is piece one. On the next page is piece two.
1
1
Great Stellated Dodecahedron made out of five pieces of paper. Cut the lines between the long and the short sides of the triangles. Fold the long lines backwards and fold the short lines forwards. N= Next part P= Previous part
N
P
Great Stellated Dodecahedron made out of five pieces of paper. Cut the lines between the long and the short sides of the triangles. Fold the long lines backwards and fold the short lines forwards. N= Next part P= Previous part
N
P
Great Stellated Dodecahedron made out of five pieces of paper. Cut the lines between the long and the short sides of the triangles. Fold the long lines backwards and fold the short lines forwards. N= Next part P= Previous part
N
P
Great Stellated Dodecahedron made out of five pieces of paper. Cut the lines between the long and the short sides of the triangles. Fold the long lines backwards and fold the short lines forwards. N= Next part P= Previous part
N
P
Great Stellated Dodecahedron made out of five pieces of paper. Cut the lines between the long and the short sides of the triangles. Fold the long lines backwards and fold the short lines forwards. N= Next part P= Previous part
N
P
Pentagonale hexacontahedron
1
2
3
4
5
6
7
8
9
10
12
Pentagonallconssitetrahedron
Stella Octangula Type 1 Type 2
Fold lines of type 1 backwards Fold lines of type 2 forwards
Fold the lines with a rightangle backwards fold the other lines forwards
Compound of two Cubes
Compound of Three Cubes (Small version)
Fold the dotted liines forwards Fold the other lines backwards
Compound of Three Cubes (Small version)
Fold the dotted liines forwards Fold the other lines backwards
D
A C
C
E
E
B
F
G G
A
B
C
A
A
A
D
E
A
A
A
F
A A
G
On this page a compound of five cubes made of one piece of paper. On the next pages a compound of five cubes made of 7 pieces of paper
Instructions: Cut and fold the piece(s) of paper. Glue the part without tabs around it last. This is the top part of piece F. This one opposites the center part of piece A. Below an example of a part
Fold forwards Fold backwards
A
B B G
C C
G
D D
F
F
E
E
B
A A
C
A
A
D
A A
E
A
A
F
A A
G
A A
Compound of five Octahedra If you use paper in five different colors each octahedron has a different color
Color 1
A
H
D
E
G
R C
B
I
U
M
P
d
N
F
O Q
Y
L
c
W
K
a S
J
Z
X
V
T
b
Compound of five Octahedra Color 2
B
K
F
G
J
W D
A
L
C
N
Q
O
E
S
R
c
d
M
P
U
T
Z X
V
b
H
I
Y
a
Compound of five Octahedra Color 3
C
L
I
J
D
K
M
B
Y
A
O
R
P
Q
S
F
G
N
E H
V
X
b
W
a
T
U
Z
d
c
Compound of five Octahedra Color 4
D
F
K
L
O
P
B
A
G
E
I
S
H
R
Q
U C
T
a
J
X
Z
d c
Y V
W
b
M
N
Compound of five Octahedra Color 5
E
G
N
O
R
H
D
A
F
B
J
T
C
V
U
I
K
W
a
S
Y
X
c
Z
b L
M
d
P
Q
Pyramids
Pentagonal pyramid
Decahedron
Rhombic Dodecahedron
Great Rhombihexacron
X
X
X
X
Fold the short lines forwards Fold the long lines backwards
Pentagonal Dipyramid
Pentakisdodecahedron X X
X
X
‘Dodecahedron’ A convex dodecahedron (not a platonic solid) constructed of 12 isosceles triangles
Hexakaidecahedron
‘Icosahedron’
A convex icosahedron (not a platonic solid) constructed of 20 isosceles triangles
Icositetrahedron
Icosioctahedron
Tricontidihedron
Tricontihexahedron
Tetracontahedron
Hecatohedron
Third Stallation of the Icosahedron Fold the dotted lines forwards Fold the other lines backwards
X X
X
X
Third Stallation of the Icosahedron Fold the dotted lines forwards Fold the other lines backwards
X X
X
X
Sixth Stallation of the Icosahedron (small version) Fold the dotted lines forwards Fold the other lines backwards First glue part A Glue the parts A-M on A
Part A:
X X
X
X
Parts B-M
Sixth Stallation of the Icosahedron (large version) First glue the parts A until F Glue the 12 other parts on the ABCDEF
C
B
D
E
A
F
Sixth Stallation of the Icosahedron (large version)
B
A
Sixth Stallation of the Icosahedron (large version)
C
A
Sixth Stallation of the Icosahedron (large version)
D
A
Sixth Stallation of the Icosahedron (large version)
E
A
Sixth Stallation of the Icosahedron (large version)
A
F
Sixth Stallation of the Icosahedron (large)
Sixth Stallation of the Icosahedron (large)
Sixth Stallation of the Icosahedron (large)
Sixth Stallation of the Icosahedron (large)
Sixth Stallation of the Icosahedron (large)
Sixth Stallation of the Icosahedron (large)
Seventh Stellation of the Icosahedron
A
D
B
B D C
B
C
G
A
A G F
C
F
I
A
A I H
H
Seventh Stellation of the Icosahedron
D
E
A
A E J
E
J
F
D
D F L
F
L
B
E
E B N
N
Seventh Stellation of the Icosahedron
G
H
B
B H O
H
O
C
G
G C Q
I
Q
J
C
C J R
R
Seventh Stellation of the Icosahedron
J
D
I
I D K
K
K
L
J
J L S
L
S
E
K
K E M
M
Seventh Stellation of the Icosahedron
M
N
L
L N T
N
T
M
O
O M F
O
F
G
N
N G P
P
Seventh Stellation of the Icosahedron
P
Q
O
O Q T
Q
T
H
P
P H R
R
R
I
Q
Q I S
S
Seventh Stellation of the Icosahedron
S
K
R
R K T
T
T
P
M
M P S
S
Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards B
B
C
C
A
D
D
E
E
F F
Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards
B
A
A
Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards
C
A
A
Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards
D
A
A
Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards
E
A
A
Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards
A
A
F
Ninth Stellation of the Icosahedron Fold the dotted lines forwards Fold the other lines backwards
C
F
B
A B
A
F
A
C
B
F
C
E
G E
G D
K D
K C
F
B
C
A
A A
C
A
D
D
E
D
E
H
I H
I G
H G
H B
C
D
E
A
E
A A
F F
A
B F
B
J
K J
K I
J I
J D
E
K
L
B
G B
G
C
G
C
H
C
C
H
D H
D L
I L
I K
L
H
F
D
K D
I
K
J
E
L
E
L
J
I J
I L
E L
E H
F
G
K
B
K
G B
L F
G
H F
H
J
I J
I L
J L
J G
K
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
A B C
F
D E
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
B A F
C
K G
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
C A B
D
G H
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
D A C
E
H I
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
E A D
F
I J
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
F A E
B
J K
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
G B K
C
L H
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
H C G
D
L I
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
I D H
E
L J
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
J E I
F
L K
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
K F J
B
L G
Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards
L G K
H
J I
Triangular prisms
Pentagonal Prism
Pentagonal Antiprism
Octagonal Prism
Octagonal Antiprism
Pentagrammic Prism Fold the dotted lines forwards Fold the other lines backwards
Pentagrammic Antiprism Fold the dotted lines forwards Fold the other lines backwards
Hexagrammic Prism Fold the dotted lines forwards Fold the other lines backwards
Hexagramic Antiprism Fold the dotted lines forwards Fold the other lines backwards
Twisted rectangular prism (45 degrees)
Twisted rectangular prism (90 degrees)
Twisted rectangular prism (+ 45 -45 degrees)
Kaleidocyclus
Caleidocyclus 8
Caleidocyclus 10
Cylinder
Tapered Cylinder
l n x
l=
c=2
x = 360.2.
r
2
+
h
2
r1
. l /c
d=c.n/l r1 r2
r1 = radius r2 = radius c = circumference of circle 1 d = circumference of circle 2 x =angel of the part of the large circle l = radius of the large circle h = height of the cone i = heigt of the tapered cylinder = pi = 3.1415
Cone
l x
l=
c=2
x = 360.2.
r
r
2
+
h
2
r
. l /c
r = radius c = circumference of the circle x =angel of the part of the large circle l = radius of the large circle h = height of the cone = pi = 3.1415
Asymetric Cone
Square Cone
Square Cone
Paper Colour 1/ papier kleur1
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
paper colour 2 / papier kleur 2
(uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
place dormerwindow
onderkant dak/
bottom roof fits around walls don't glue roof on the walls
Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
Paper Colour 1/ papier kleur1
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
Paper Colour 1/ papier kleur1
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
Paper Colour 1/ papier kleur1
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
Paper Colour 1/ papier kleur1
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof fits around walls don't glue roof on the walls (uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
place dormerwindow Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof fits around walls don't glue roof on the walls (uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
place dormerwindow Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof fits around walls don't glue roof on the walls (uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
place dormerwindow Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof fits around walls don't glue roof on the walls (uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
place dormerwindow Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
Globe
3
1
1
3 1
1 2
2
3 2
3
1
1
3 1
2
3
2
1
1
2
2
3
1 2
3
2
1
1
1
3
2
3
1
3
3
2
3
2
2
3 2 3 1
1 2
3 2
Large Chevaux-de-frise The other two parts are on the next two pages
3
1
1
1
2
2
3
2
2