# Dodecahedral Surprise!

*Enjoy the phenomena you witness here!*After doing so, please answer the questions that follow.

**To explore this phenomenon within GeoGebra Augmented Reality**, see the directions below the questions and first video.

## 1.

Suppose the length of the **purple segment** is * a*.
Express the distance from the center of the dodecahedron to any vertex

**in terms of**.

*a*## 2.

Express the **distance between any 2 adjacent vertices** of this regular dodecahedron **in terms of a**.

## *3.

How does **your answer for (2)** relate to the value of the golden ratio?

## TO EXPLORE IN AUGMENTED REALITY:

1) Open up GeoGebra 3D app on your device.
2) Go to MENU (upper left corner).
Go to OPEN. Under Search, type

**Mt3TwsUK**. Find the slider named**h**and slide it slowly.