Face Probabilities of Archimedean Solids

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SUMMARY

This discussion focuses on calculating the probabilities of Archimedean Solids, such as the snub cube and truncated icosahedron, landing on specific faces when rolled. Key factors include face area, edges, and vertices, with an emphasis on how these parameters influence the probability outcomes. The conversation highlights the importance of considering real-world factors like drag forces and weight, which can alter theoretical probabilities. Participants seek existing research or keywords for further exploration on platforms like arXiv.

PREREQUISITES
  • Understanding of Archimedean Solids and their geometric properties
  • Basic knowledge of probability theory and statistical analysis
  • Familiarity with physical dynamics, including drag forces and weight
  • Experience with academic research methodologies and literature searches
NEXT STEPS
  • Research "probability calculations for irregular polyhedra" in academic journals
  • Explore "geometric probability" and its applications in physical simulations
  • Investigate "drag force effects on rolling objects" in physics literature
  • Study "Archimedean Solid properties" for deeper geometric insights
USEFUL FOR

Mathematicians, physicists, and hobbyists interested in geometric probability, as well as researchers looking to explore the dynamics of rolling polyhedra.

Spinalcold
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I'm looking for a way to calculate the probabilities of Archimedean Solids landing on a specific face if a person would roll one. Of course, not the regular polygons like cubes and dodecahedrons, but something with more than one type of face like the snub cube or truncated icosahedron.

I am wondering of the edges and vertices would need to be calculated as well as face area, or if the area would be enough to get a good approximation of this. If area is the dominant parameter on this it would be interesting that size determines the probability in an ideal situation. Of course, in reality it wouldn't be ideal and drag forces (and weight of the object) would change these probabilities as well.

If this has already been studied (and I'm guessing it likely has been), I'd be grateful for links to papers, or even the appropriate key words to search for on arXiv.

Thanks!
 
Physics news on Phys.org
https://www.quora.com/How-does-one-calculate-the-probability-that-an-irregular-polyhedron-when-rolled-lands-on-a-particular-face
 
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