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Here are shadows of some 3D shapes. What shapes could have made them?

# Skeleton Shapes

##### Stage: 1 Challenge Level:

We had lots of correct solutions to this problem and you used many different ways of helping yourselves to reach the answers. Some of you made the shapes from straws and modelling clay, like Rachel, Abigail and Alistair from Histon and Impington Infant School. They sent in a photo of their models:

Others of you decided to make the shapes from Polydron, while some of you drew the shapes carefully. Alice from Tattingstone, and Scarlett and Sam from Cupernham, were among those who opted for drawing, but William, also from Cupernham sent in particularly careful sketches using isometric paper:

Cuboid : 8 balls, 12 straws

Hexagonal prism : 12 balls, 18 straws

Square pyramid : 5 balls, 8 straws

Tetrahedron : 4 balls, 6 straws

Triangular prism : 6 balls, 9 straws

Chris and Michael from Moorfield Junior School also sent some excellent drawings and took the problem a step further by looking at the relationship between the number of faces, edges and vertices of different prisms. They enclosed this table:

Type of prism Faces Vertices Edges
triangular 5 6 9
cube or cuboid 6 8 12
pentagonal 7 10 15
hexagonal 8
12
18
heptagonal 9 14 21
octagonal 10 16 24
nonagonal 11 18 27
decagonal 12 20 30

Chris and Michael say:

There are patterns you can see in the vertices and edges columns. The number of vertices is double the amount of sides on the 2D shape at each end. In the edges column it's three times the amount of sides on the 2D shape.

Perhaps you can spot some more patterns too. Let us know if so.

Thank you also to these people who sent us correct answers too:

Hugo, Emile and Benny from Wesley College Prahran Preparatory School in Melbourne, Australia.
Charlotte and Thomas.
Al from Dudley.
Ryo, Jake and Charlie from Moorfield Junior School.
Samuel from Bispham Drive Junior School in Nottingham.
David from Tithe Barn Primary School.