Paper Models of Polyhedra

Home , Antiprism, Cuboctahedron, Decahedron, Dodecahedron, Great dodecahedron, Icosahedron

Gijs Korthals Altes

Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia Copyrights © 1998-2001 Gijs.Korthals Altes All rights reserved . It's permitted to make copies for non-commercial purposes only email: [email protected].net Paper Models of Polyhedra

Platonic Solids Dodecahedron Cube and Tetrahedron Octahedron Icosahedron

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 11 7 5

9. 12 2 4 10 6.

8 Dodecahedron Dodecahedron Cube

Tetrahedron 4 Cube

5 1 2 6

4 3 Tetrahedron

2 1 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 7 13

5 12

10 1

3 4

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

F C

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. 1 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 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

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

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

F G

G A B

A A D

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 B A B

G C C G

E E B

A A C

A A E

A G

A Compound of five Octahedra If you use paper in five different colors each octahedron has a different color

Color 1

A D H G

E R

C I

B U

M d P F N O

Y Q

L c

W K a T J S

X Z

V b Compound of five Octahedra

Color 2

B F K J G W

D A

C L

N O Q S E R d c

M P

U T Z Y V X

H b

I a Compound of five Octahedra

Color 3

C I L D

J K

B M

Y A

O P R Q F S

G N

E H

V X b Z W a

T d

U c Compound of five Octahedra

Color 4

D K F O

L P

A B

E G

I H S R

U Q

C T

J a

X Z d b Y c

V M

W N Compound of five Octahedra

Color 5

E N G R

O H

D F

A B

J C T V I U

K a

W S

Y X c d Z b

L P

M Q Pyramids Pentagonal pyramid Decahedron Rhombic Dodecahedron Great Rhombihexacron

Fold the short lines forwards Fold the long lines backwards Pentagonal Dipyramid Pentakisdodecahedron 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 Third Stallation of the Icosahedron Fold the dotted lines forwards Fold the other lines backwards

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 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

B D

F Sixth Stallation of the Icosahedron (large version)

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 D

C C

B G

A G

F F

C I

A I

H H Seventh Stellation of the Icosahedron

D E

A E

J J

E F

D F

L L

F B

E B

N N Seventh Stellation of the Icosahedron

G H

B H

O O

H C

G C

Q Q

I J

C J

R R Seventh Stellation of the Icosahedron

J D

I D

K K

K L

J L

S S

L E

K E

M M Seventh Stellation of the Icosahedron

M N

L N

T T

N M

O M

F F

O G

N G

P P Seventh Stellation of the Icosahedron

P Q

O Q

T T

Q H

P H

R R

R I

Q I

S S Seventh Stellation of the Icosahedron

S K

R K

T T

T P

M P

S S Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards

B B

D A

F F Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards

A Eighth Stellation of the Icosahedron (Large version) Lold dotted lines forwards Fold other lines backwards

F Ninth Stellation of the Icosahedron Fold the dotted lines forwards Fold the other lines backwards

C F

B A

A F B C F C

E G

D K D K C F

B C

A A

C D D E

D E

H I

G H G H B C

D E

A A

A A E F F B

F B

J K

I J I J D E K L

B G

G C H C C C

H D

L I L I K L

H F

D K

I E J L

E L

J I

L E L E H F

G K

B G

B G K L F H

F H

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

F D

E Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

B A

C K

G Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

C A

D G

H Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

D A

E H

I Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

E A

F I

J Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

F A

B J

K Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

G B

C L

H Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

H C

D L

I Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

I D

E L

J Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

J E

F L

K Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

K F

B L

G Final Stellation of the icosahedron Fold the dotted lines forwards Fold the other lines backwards

L G

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 2 2 l = r + h

c = 2 r1 x = 360.2. . l / c d = c . n / l r1 r1 = radius r2 = radius r2 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 2 2 l = r + h

c = 2 r x = 360.2. . l / c

r = radius c = circumference of the circle r 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 dormer- window 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

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

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

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 dormer- window

Twee zijden dak Two sides of the roof

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 dormer- window

Twee zijden dak Two sides of the roof

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 dormer- window

Twee zijden dak Two sides of the roof

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 dormer- window

Twee zijden dak Two sides of the roof

paper colour 2 / papier kleur 2 Globe 3 1 3 1 2 2

3 1 3 1 2 2

3 1 3 1 3 1 3 2 2 1 2 2

3 1 3 1 2 2

3 1 3 1 2 2 3 1 3 1 2 2 Large Chevaux-de-frise The other two parts are on the next two pages

1 1 1

2 2 3

2 2