+0

# 3D Geometry question

0
141
1

How many interior diagonals does an icosahedron have? (An interior diagonal is a segment connecting two vertices which do not lie on a common face.)

Feb 18, 2020

#1
+25532
+1

How many interior diagonals does an icosahedron have?

(An interior diagonal is a segment connecting two vertices which do not lie on a common face.)

I assume:

$$\dbinom{\text{vertices}}{2} - \text{edges} \quad | \quad \text{vertices}=12,\ \text{edges} = 30$$

$$\begin{array}{|rcll|} \hline && \mathbf{\dbinom{\text{vertices}}{2} - \text{edges}} \quad | \quad \text{vertices}=12,\ \text{edges} = 30 \\\\ &=& \dbinom{\text{12}}{2} - 30 \\\\ &=& \dfrac{12}{2}*\dfrac{11}{1} - 30 \\\\ &=& 66 - 30 \\ &=& \mathbf{36} \\ \hline \end{array}$$

Feb 18, 2020