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?
Ah, tesselations! They can be quite puzzling, can't they? Don't worry, my friend, I'm here to help you out with a touch of humor!
So, the notation of schlafli {3,3,4,4} refers to the number of sides each polygon has around each vertex in the tesselation. In this case, it means that at each vertex, you'll have three triangles, three more triangles, followed by four squares, and finally, four more squares. Quite the party of shapes!
Now, drawing a tesselation can be a bit tricky without visuals, but imagine placing these shapes together, starting from one vertex, and repeating the pattern. Triangles connect to triangles, squares to squares, creating a beautiful, repeating pattern.
As for your second question, the schlafli notation can indeed apply to regular and semi-regular tesselations, but it can also be used to describe non-regular tesselations as well. It's a versatile notation that can handle all sorts of polygonal shenanigans!
I hope this helps you, my friend. Just remember, embrace the shapes, dance with the polygons, and tesselate like nobody's watching!
To answer your first question, a tesselation with the Schlafli notation of {3,3,4,4} means that the pattern consists of polygons with 3 sides, polygons with 3 sides, polygons with 4 sides, and polygons with 4 sides meeting at each vertex.
To draw a tesselation with this notation, you can start by drawing a polygon with 3 sides as the base shape. Then, each vertex of this polygon will have one triangle (3-sided polygon), another triangle, a quadrilateral (4-sided polygon), and another quadrilateral meeting at it. Repeat this pattern to fill the space without any gaps or overlaps. The resulting tesselation will consist of triangles and quadrilaterals.
Regarding your second question, the Schlafli notation applies to various types of tesselations, including regular and semi-regular tesselations. However, it is not limited to only those types. The Schlafli notation can describe any type of tesselation, including irregular or non-uniform tesselations. It simply represents the number of sides of each polygon at the vertex in the tesselation.
To answer your first question, the Schlafli notation {3,3,4,4} refers to the pattern of polygons that meet at each vertex in a tessellation. Let's break it down:
The first number (3) represents the number of triangles that meet at each vertex.
The second number (3) represents the number of triangles that meet around each vertex.
The third number (4) represents the number of squares that meet around each vertex.
The fourth number (4) represents the number of squares that meet at each vertex.
Based on this notation, we can determine the shapes present at each vertex. In this case, there will be three triangles and four squares meeting at each vertex.
To draw a tessellation with this Schlafli notation, you can start by drawing a triangle. Then, attach three more triangles to each of its edges, forming a larger triangle at each vertex. Finally, attach four squares to the sides of the larger triangles, creating your tessellation.
Regarding your second question, the Schlafli notation can be used to describe regular and semi-regular tessellations, as well as certain types of irregular tessellations. Regular tessellations are made up of identical regular polygons that meet at each vertex in a consistent pattern. Semi-regular tessellations have different types of regular polygons that meet at each vertex in a repeating, non-repetitive pattern. Irregular tessellations are more flexible and can contain a combination of regular and irregular polygons meeting at each vertex. Therefore, Schlafli notation can be applied to all three types of tessellations.