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What polygons can be used to make tessellations?
Regular tessellations can be made using triangles, squares, and hexagons.
Which shapes have all sides equal?
All regular polygons. But there are also others which look like squashed versions of regular polygons. A "squashed" square makes a rhombus. Similarly there are squashed polygons with larger numbers of sides. They should be called equilateral polygons, but that phrase is not much used.
Which regular polygons will fit together to tile a surface?
It depends on the shape of the surface Flat surface can be tiled by triangles, squares, and hexagons, these are the only combinations for the regular tessellations. semi-regular tessellations (where multiple polygons are used in the same tiling) There are in fact an infinite number of possible tessellations. All polygons can work from triangles to approaching a circle... a circle tiling would require an infinite number of infinitesimally small polygons around it, so you may or may not consider this a possibility. NOT all polygons can be in the same tessellations, for example triangles, heptagons, and 42-gons cannot be in a 1:1:1 ratio. In 3 dimensions regular polygons can be perfectly assembled into only 5 regular polyhedrons (3d version of polygon) (the platonic solids - these have been used to represent the elements, fire water, earth air and space) tetrahedron consists of 4 triangles cube (hexahedron) consists of 6 squares octahedron 8 triangles dodecahedron 12 pentagons icosahedron 20 triangles The hexagon didn't make it... possibly an infinite number of would assemble a sphere of infinite diameter, but this has never been included in any lists I've run across. In 4 dimensions, there are six convex 4-polytopes, called (polychorons), the smallest of which is called the pentatope, and is composes of 10 triangles, which can only be done in 4 dimensions, it can't be constructed under normal circumstances in our worlds. In 5, 6, 7, 8, 9, and 10 dimensions that are only 3 regular n-polytopes for each respectively... this may continue indefinitely but I don't know how to prove this, it's probably been done. If it does continue toward infinite dimensions that 2 and 3 dimensions are "special" and perhaps that is why we find ourselves in such a universe.
What is the angle sum around a vertex in a tessellation?
In a tessellation, the angle sum around a vertex depends on the type of polygons used in the tessellation. For regular polygons, the angle sum around a vertex is always 360 degrees. This is because each interior angle of a regular polygon is the same, so when multiple regular polygons meet at a vertex in a tessellation, the angles add up to 360 degrees.
Why each letter in polygons name used only once?
polygons are polygons u willl find the answer here trust me each letter in polygons name used only once because it is a word
