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Homework Help Forum: Mathematics
Current Questions | Post a New Question
Answer this Question | Further Reading

Posted by Stine on Wednesday, February 7, 2007 at 9:04pm.

I have this question on tesselations,
I got some homework and one of the questions are:

A tesselation with the notation of schlafli of {3,3,4,4}.
What formes are at the vertex.
Draw a tesselation of it.

I have been trying to figure this out for 30mins now and i just can't figure it out.

Another question,
Do the schlafli notation's only apply to regulier and and semi-regulier tesselations?

way to copy and paste bro XD

To answer the first question, we need to understand what the Schlafli notation {3,3,4,4} means. The Schlafli notation is a way to describe the polygonal patterns in a tiling or tessellation. In this case, the numbers in the notation represent the number of sides of the polygons that meet at each vertex.

In the notation {3,3,4,4}, the first two numbers, 3 and 3, indicate that there are two types of polygons with 3 sides (triangles) meeting at each vertex. The next two numbers, 4 and 4, indicate that there are two types of polygons with 4 sides (squares) meeting at each vertex.

So, to answer the question, at each vertex of this tiling, there will be two triangles and two squares.

To draw the tessellation, you can start by drawing a triangle. Then, connect the midpoints of each side of the triangle to form a smaller triangle inside. Repeat this process for each smaller triangle until the tessellation is complete. Finally, draw squares on the sides of each smaller triangle, connecting to the adjacent triangles. This will create a tessellation with the Schlafli notation {3,3,4,4}.

Regarding your second question, the Schlafli notations can be used to describe regular and semiregular tessellations. Regular tessellations are those in which the same regular polygon meets at each vertex, such as {3,3,3,3} for a tessellation with equilateral triangles. Semiregular tessellations are those in which more than one type of regular polygon meets at each vertex, such as {3,6,6} for a tessellation with equilateral triangles and regular hexagons.

In summary, the Schlafli notation can be used to describe both regular and semiregular tessellations.