WOLFRAM|DEMONSTRATIONS PROJECT

Deforming Nets of Polyhedra

​
Dodecahedron
net
labels
deformed net
new net
1
2
3
4
5
6
7
8
9
10
11
12
index of moved face F
1
2
3
4
5
6
7
8
9
10
11
12
index of face G on which to glue F
1
2
3
vertices of common edge
1
{8,9,10,11,12}
2
{3,4,5,6,7}
3
{2,4,7,10,11}
4
{2,3,5,11,12}
5
{2,4,6,8,12}
6
{2,5,7,8,9}
7
{2,3,6,9,10}
8
{1,5,6,9,12}
9
{1,6,7,8,10}
10
{1,3,7,9,11}
11
{1,3,4,10,12}
12
{1,4,5,8,11}
moved face: 1
{15,10,9,14,1}
glued-on face: 2
{2,6,12,11,5}
indices of two
vertices of the face
{2,3}
Select a polyhedron to draw its net. To deform it, choose a face
F
to move, a target face
G
to attach
F
, and the edge of
G
where
F
is attached. To make this easier, the adjacency relation of the faces is displayed.
Warning: some possible deformations produce a figure that is no longer a valid net.