Tessellations: If I split a square into four equilateral triangles...

[Dr. T]

Hi!


If I split a square into four equilateral triangles, paint each triangle in a different color, and the create a tessellation with the the squares, what type of tessellation is it? Regular? Semi-regular?


Thank you!


Doctor T

 

[mmm4444bot]

If I split a square into four equilateral triangles, paint each triangle in a different color, and the create a tessellation with the the squares, what type of tessellation is it? Regular? Semi-regular?

Do you mean isosceles triangles?

See: http://www.mathsisfun.com/geometry/tessellation.html :cool:

 

[Dr. T]

Do you mean isosceles triangles?

See: http://www.mathsisfun.com/geometry/tessellation.html :cool:

Dear mmm4444bot:

Oops! Yes, four isosceles triangles with one 90 degrees angle and two 45 degrees angles each.

FYI, prior to posting, I had viewed the Math Is Fun website. However my tessellation does not EXACTLY match the definitions of a regular tessellation or of an irregular tessellation.

Doctor T

 

[Dr. T]

So you simply drew the 2 diagonals inside the square,
which of course cross at center of square: right?

Doctor D

Dear Denis,

Yes.

Doctor T

 

[Otis]

... my tessellation does not EXACTLY match the definitions of a regular tessellation or of an irregular tessellation ...

Agree. There's only one shape (isosceles triangle). The vertex in the center of a "square" is associated with four triangles, but other vertices are associated with eight triangles.

I vote for "demi-regular". A number of sites note that its definition is not well-defined, like wolframalpha:

"A demiregular tessellation, also called a polymorph tessellation, is a type of tessellation whose definition is somewhat problematical."

Seems to fit.

 

[Dr. T]

Agree. There's only one shape (isosceles triangle). The vertex in the center of a "square" is associated with four triangles, but other vertices are associated with eight triangles.

I vote for "demi-regular". A number of sites note that its definition is not well-defined, like wolframalpha:

"A demiregular tessellation, also called a polymorph tessellation, is a type of tessellation whose definition is somewhat problematical."

Seems to fit.

Dear Otis,

I agree. As you pointed out, although there is only one shape (an isosceles triangle), there are vertices with four triangles and vertices with eight triangles. Thus, not a regular tessellation.

Doctor T