This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Penta people, the Pentigles, always build their houses from five
square rooms on one level - ground level.
The houses can be designed in a variety of shapes, but a room
must be joined to at least one other room by one wall.
Here is a design drawing for a Penta house, a view from
Here is another one:
There are many different ways that you can arrange the five
I wonder how many different Penta homes you can create.
Try to find all possible shapes the Pentigles can build their
New homes are being built in Penta Place.
The homes are built right next to each other and are arranged
and fitted together to create other shapes. Experiment and see what
shapes you are able to make.
Penta Place will use just one shape that can be made, the
See if you can solve some of the Penta's challenges below.
Find three of the Penta house shapes that you created and fit
them together to form a 3X5 rectangle like this one.
I wonder if you could make other sized rectangles using three of
the Penta shapes.
Are you able to find four of the Pentigles' house shapes to make
a larger rectangle like this?
Here we have a 5 by 5 square. Construct a similar square with
five of the Penta houses.
If you are unable to do these activities, check that you have
made all of the Pentigles' house shapes that you possibly can.
There are in fact 12 different shapes. Have you found all of
Now, try to find six of the Penta houses and arrange them to fit
into a 5X6 rectangle like this one.
This arrangement might require a more work, but can you find
eight of your Penta designs to recreate a 40 room unit arranged in
an 5X8 rectangle?
I wonder whether a rectangle can be constructed using 9, 10 or
11 of the Penta shapes....
By now you should have managed to find all of the Penta
This large rectangle is made from 60 rooms. Here is a very
difficult challenge! Can you use all 12 Pentomino shapes to make a
similar rectangular arrangement.
I wonder what results you would get if you arranged
the houses into shapes other than rectangles .....