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Knoblauch's picture

Dodecahedron is one of the five Platonic Solids. It consists of

  • 12 faces (congruent pentagons)
  • 30 edges
  • 20 vertices (the meeting of 3 faces)


From Trigonometry

A basic pentagon can be created from the basic code

note: the internal angle of a regular pentagon is 108o, making the external angle, which we are are turning, 72o

from this initial pentagon, we need to create pentagons connecting to our 5 initial edges. To do this, we need to consider what angle these are to be connected at. The dihedral angle of a dodecahedron is116.56505° = arccos(-1/√5), meaning that we need to tilt down 63.43495o

this process needs to be repeated several times to create all edges of our dodecahedron. The final code would look something like.


EleanorNwtn's picture

Its quite difficult to do it

Its quite difficult to do it , Still not able to get the concept clearly.


Knoblauch's picture

start small

By the time I attempted the dodecahedron, I had already worked my way through the simpler platonic solids. This allowed me to familiarise myself with the coding whilst creating solids which I found easy to understand. There were still a lot of false starts and editing before I succesfuly completed the dodecahedron.

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