Maths Feast 2016 Practice Comprehension Round
Instructions and Answers
Instructions
Give each team the poster and about 3 minutes to study it before giving the team the questions.
Teams should be able to look back at the poster for reference throughout the round.
1. Complete the following table of information:
Net
3-D View
Name
Schlegel
Diagram
F= 6
E=12
Cube
V=8
(1 mark)
(1 mark)
(1 mark)
Square
based
pyramid
F=5
E= 8
V=5
(1 mark)
(1 mark)
(1 mark)
F=8
E=12
Octahedron
V= 6
(1 mark)
(1 mark)
F=5
Triangular
Prism
E=9
V=6
(1 mark)
(1 mark)
(1 mark)
(1 mark)
F=4
Regular
E=6
Tetrahedron
V=4
(1 mark)
(1 mark)
__
15
(1 mark)
2.
A polyhedron has 7 faces and 15 edges.
V=10 (1 mark)
How many vertices does the polyhedron have?
Name the polyhedron.
Pentagonal Based Pyramid (1 mark)
Draw a net of the polyhedron.
If the team draws a
correct net and
Schlegal diagram for
an incorrectly named
polyhedron they
score 2 marks.
(1 mark)
Draw a Schlegel diagram of the polyhedron.
(1 mark)
__
4
3.
A polyhedron has 7 vertices and 12 edges.
F = 7 (1 mark)
How many faces does the polyhedron have?
Name the polyhedron.
Hexagonal Based Pyramid (1 mark)
Draw a Schlegel diagram of the prism.
If the team draws a
correct Schlegal
diagram for an
incorrectly named
polyhedron they
score 1 mark.
(1 mark)
4.
If a vertex is placed at the centre of each square face of a cube and each adjacent vertex is joined,
an octahedron is created inside the cube. The octahedron is said to be the dual of the cube (and
vice versa).
How many faces, edges and vertices does a cube have?
F=6, V=8, E=12 (1 mark)
How many faces, edges and vertices does an octahedron have?
F =…..,
V= …..,
E
F=8, V=6, E=12 (1 mark)
= …..
How could this show that an octahedron is the dual of a cube?
F =…..,
V= …..,
Vertices on the cube = Faces on the Octahedron; Vertices on the Octahedron = Faces
on the Cube
Edges are the same on both.
(1 mark)
= …..
E
This is the outside 3-D
view of a dodecahedron.
How many faces, edges and vertices does a dodecahedron have?
F=12, V=20, E=30 (1 mark)
F =…..,
= …..
This is the outside 3-D
view of an icosahedron.
V= …..,
E
F=20, V=12, E=30 (1 mark)
How many faces, edges and vertices does an icosahedron have?
How could this show that a dodecahedron is the dual of an icosahedron?
Vertices on the dodecahedron = Faces on the icosahedron;
Vertices on the icosahedron = Faces on the dodecahedron;
Edges are the same on both.
F =…..,
= …..
V= …..,
E
(1 mark)
What is the dual of a tetrahedron? Explain why?
It is the dual of itself
__
(1 mark)
because number of vertices = number of faces.
(1 mark)
8