Hi,
Can somebody plz tell me:

How many cubes are present in a 4d-hypercube?

My answer is 3. I got it from the following link:
https://en.wikipedia.org/wiki/Hypercube


Zulfi.

 

How do you get 3 from that reference. They explicitly give a different number.

 

Hi,
Thanks for your response. Sorry I dont see their answer. Kindly guide me.

Zulfi.

 

Since the 4th dimension is beyond anyone's experience, all we can do is look at 3D shadows of 4D objects. The tesseract is the simplest object to view.
To find out how many cubes are in a tesseract, go to the table in the middle of the web page. On the row that says 4-cube, look for the column that says cells. That is the number of cubes in a tesseract.

 

Hi,
Thanks. It says 8.

Zulfi.

 

Or draw the 3D projection of a tesseract and count the cubes directly. There is the inner cube, the outer cube (2 cubes) plus the projection between each of the 6 faces of these cubes (6 more cubes) giving 6+2=8.

 

Hi,
I would try. But i have one related question. Are hypercubes possible in a 3d environment?

Zulfi.

 

The 3-D projection of a 4-D object is a 3-D object. Think of it like a "shadow". You are a 3-D object but your shadow is a 2'-D object. The shadow of an n-D object is an object in (n-1) dimensions.

 

Hi,
Thanks for your reply.

Zulfi.