** **

*Task developed by Giacomo Rotolo-Ross, University of Sydney, 2020*

2

**QUESTION ONE **

ROLL UP, ROLL UP

**9 MARKS **

When one thinks of

**numbers **and **βchanceβ**, a dice is the first thing that comes to mind. Almost everyone, it can be said with certainty, will picture ab six-sided one. Dice with more or less sides

**do exist **but are **very uncommon, **and at the most they might have a few extra sides β perhaps 12 at the maximum.

**Dice Lab, **however, a small Arizonan company, had other ideas, and set about creating a sided dice back in

2016. The mathematical name for this shape is ab disdyakis triacontahedron, and this is

the focus of the present task 1. How many edges does a disdyakis triacontahedron have ______________

**(1 mark)** 2. How many vertices does the shape have _______________

**(1 mark)** 3. What type of triangles are the faces _______________

**(1 mark)** 4. Which feature of the shape does the equation below represent _________

**(1 mark)** 180 11 (5 + 4

β5)

5. Which feature of the shape does the equation below represent ________

**(1 mark)** 180 11

οΏ½179 β 24β5 6. Complete the equation, which represents the number of possible combinations of numbers from 1 to 120 that

could be placed on the shape, by inserting a number in the brackets

**(3 marks)**.

ππ = 10

( )

7. The above number is greater than the estimated number of atoms in the universe. True or false _________________

**(1 mark)**