Slicing dice and cutting corners

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SUMMARY

The discussion focuses on the geometric transformation of a standard six-sided die when its corners are cut. Initially, a die has 6 sides, and after the first cut, it increases to 14 sides. Subsequent cuts add more sides, with the formula for the minimum number of sides after n cuts being 6 + 8 + 12 for the first two cuts. Participants also suggest exploring similar transformations on a tetrahedron to understand the relationship between cuts, vertices, and edges.

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  • Familiarity with the concept of vertices and edges in geometry.
  • Knowledge of geometric transformations and their effects on shapes.
  • Basic mathematical skills for calculating sides after multiple cuts.
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  • Research the geometric properties of polyhedra, focusing on the effects of truncation.
  • Explore the Euler characteristic for polyhedra to understand vertices, edges, and faces.
  • Learn about the geometric transformations applicable to tetrahedrons and other polyhedra.
  • Investigate computational geometry techniques for modeling and visualizing shape transformations.
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Mathematicians, geometry enthusiasts, educators teaching geometric transformations, and anyone interested in the properties of polyhedra.

Sariaht
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A dice has 6 sides.
If you cut the corners of a dice you get 6 + 8 = 14 sides.
If you cut again, the minimum number of sides you get is 6 + 8 + 12.
If you cut n times, what is the minimum number of sides you get?
 
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Sariaht said:
A dice has 6 sides.
If you cut the corners of a dice you get 6 + 8 = 14 sides.
If you cut again, the minimum number of sides you get is 6 + 8 + 12.
If you cut n times, what is the minimum number of sides you get?

Perhaps you could try to figure this out for a tetrahedron (a triangular pyramid) first?
Can you predict how many vertices the resulting shape will have after each cut?
Does it matter how many edges meet at each vertex?
 
Good idea!
 

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