Slicing dice and cutting corners

Starting with a tetrahedron, cutting the corners would result in a shape with 4 + 6 = 10 sides. Cutting again would give a minimum of 4 + 6 + 12 = 22 sides. For any number of cuts, the minimum number of sides can be calculated by multiplying the number of cuts by 12 and adding 4. The number of vertices would also increase by the same amount. The number of edges meeting at each vertex does not affect the minimum number of sides. In summary, cutting a dice or tetrahedron multiple times will result in a shape with a minimum of 12n + 4 sides, where n is the number of cuts made.
  • #1
Sariaht
357
0
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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  • #2
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?
 
  • #3
Good idea!
 

FAQ: Slicing dice and cutting corners

What is the difference between slicing, dicing, and cutting?

Slicing, dicing, and cutting are all methods of food preparation that involve cutting ingredients into smaller pieces. Slicing involves cutting ingredients into thin, flat pieces, while dicing involves cutting ingredients into small, cube-shaped pieces. Cutting refers to any method of dividing an ingredient into smaller pieces, and can include slicing, dicing, or other methods such as chopping or mincing.

What tools are used for slicing, dicing, and cutting?

Common tools used for slicing, dicing, and cutting include knives, mandolines, food processors, and vegetable peelers. The specific tool used will depend on the type of ingredient being prepared and the desired size and shape of the pieces.

How can I ensure consistent and even slices and cuts?

Consistent and even slices and cuts can be achieved by using a sharp knife and applying even pressure while cutting. It can also be helpful to use a guide, such as a ruler, to ensure uniform pieces. Using a mandoline or food processor with adjustable thickness settings can also help achieve consistent slices and cuts.

What are some safety precautions to take when slicing, dicing, and cutting?

To avoid injury, it is important to always use sharp knives and keep fingers and hands away from the blade while cutting. It is also important to use a stable cutting surface and to hold the ingredient securely while cutting. Properly storing and handling knives and other cutting tools can also help prevent accidents.

Are there any tips for maximizing efficiency when slicing, dicing, and cutting?

To increase efficiency, it can be helpful to have all ingredients prepped and ready to be cut before starting. This can include washing, peeling, and trimming the ingredients. Additionally, using appropriate tools for the job and practicing proper cutting techniques can also help save time and effort.

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