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.