Polychora

wintersolstice · 2009-06-07 22:31:31

I read some info about polychora (4D Polytopes) and have read that the 4D analog to a icosahedron has 600 cells (which are tetrahedra) but when I tried to prove it I came up which several values (none of which were 600!) The other principle is that it has 5 faces at each edge.

Can anyone explain why it's 600?

and the self dual regular polychoron which uses octohedral cells has 24 cells. Why?

I also wouldn't mind knowing the pronunctiation of "polychoron" I think it's "poly-kor-on" but I'm not sure.

integer · 2009-06-09 01:18:49

A google search will give a lot of information and some of the facet/edge/lines count.

chillyt · 2009-06-09 01:34:20

500 cm cubic that is as cost efficient as possible. Should she use a square- based prism box or a cylinder for the cables? Justify your answer mathematically.

#2
Extra fuel tanks carried in the cabin of a plane called ferry tanks.These tanks allow a plane to fly greater distances. A cylindrical ferry tank needs to hold 600 L of aircraft fuel.

a) What are the dimensions of two possible cylindrical fuel tanks?

b) What should the dimensions of the tank be to minimize the amount of aluminum used in its construction?

c) How do these dimensions compare to the optimal square-based prism fuel tank?

#3
Determine the dimensions of the cylinder of maximum volume that can be inscribed in a sphere of radius 8 cm.

#4
An open- topped cylinder is to be made using 500 cm square of plastic.

a) Describe how you would determine the dimensions of the cylinder of maximum volume.

b) Determine the dimensions of the cylinder with the optimal volume. Round to the nearest tenth of a centimetre.

#5
RiceCo ships long- grain rice in large cardboard boxes that hold 216 000 cm cubic square root.
Determine the least amount of cardboard needed for one of these boxes, if an extra 10% is used to join the sides of the boxes.

#6
At the Besutiful Box Company, cardboard boxes must hold 2700 cm cubic square root. Determine the least amount of cardboard needed for one of these boxes if the boxes have right- triangular flaps to fasten the faces together. The triangular flaps are all the same size with one leg equal to one third the length of the box and the other leg equal to one third the width of the box.

#7
A warehouse is designed to provide 1000 m cubic root of storage space. The surface area of the walls and roof must be kept to a minimum to minimize heat loss. Very little heat is lost through the floor, so you can ignore it. Carry out an investigation to determine the best dimensions for the warehouse.

wintersolstice · 2009-06-09 21:12:56

integer wrote:

A google search will give a lot of information and some of the facet/edge/lines count.

integer wrote:

A google search will give a lot of information and some of the facet/edge/lines count.

I already know what the count is (edges faces etc) I want to know where they come from. I can prove that it is:

X is 120. why?

Math Is Fun Forum

#1 2009-06-07 22:31:31

Polychora

#2 2009-06-09 01:18:49

Re: Polychora

#3 2009-06-09 01:34:20

Re: Polychora

#4 2009-06-09 21:12:56

Re: Polychora

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