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What ways are there to fit four polygons around a vertex?
There are infinitely many even on the plane and infintely more in space.For Example:Take a square, draw the diagonals.The meeting point of the dialgonals is the vertex where three polygons (in this case triangles) meet.
What is the maximum number of regular polygons that can be arranged around a single point?
6 (triangles).
Do regular polygons have point symmetry?
yes
Will a regular polygon tile?
There are only three regular polygons which with tile. These a re a triangle, quadrilateral (square) and hexagon.This is because if there are n tiles meeting at a point, then the sum of the angles around that point must be 360 degrees - otherwise the polygons will overlap. The only regular polygons with interior angles that are factors of 360 are the ones mentioned above.
Why will only three of the regular polygons tessellate the plane?
The tessellating polygons must meet at a point. At that point, the sum of the interior angles of the polygons must 360 degrees - the sum of angles around any point. Therefore, each interior angle must divide 360 evenly. There is no 1 or 2 sided polygon. The interior angle of a regular pentagon is 108 degrees which does not divide 360 degrees. The interior angles of regular polygons with 7 or more sides lie in the range (120, 180) degrees and so cannot divide 360.That leaves regular polygons with 3, 4 or 6 sides.
Is a vertex is a regular polygon?
A vertex is the point where two (or more) lines meet. Polygons have vertices.
What ways are there to fit four polygons around a vertex?
There are infinitely many even on the plane and infintely more in space.For Example:Take a square, draw the diagonals.The meeting point of the dialgonals is the vertex where three polygons (in this case triangles) meet.
What is the maximum number of regular polygons that can be arranged around a single point?
6 (triangles).
Do regular polygons have point symmetry?
yes
Will a regular polygon tile?
There are only three regular polygons which with tile. These a re a triangle, quadrilateral (square) and hexagon.This is because if there are n tiles meeting at a point, then the sum of the angles around that point must be 360 degrees - otherwise the polygons will overlap. The only regular polygons with interior angles that are factors of 360 are the ones mentioned above.
Which shape has more than one vertex?
A vertex is the point at which two edges meet such as a corner. Shapes that have more than one vertex includes polygons. Triangles, rectangles, and octagons have more than one vertex.
Which polygons cannot be used to form a regular tesselation?
Most regular polygons will not tessellate but if their interior angles is a factor of 360 degrees then they will tessellate or if their angles around a point add up to 360 degrees then they also will tessellate.
Explain why regular polygons with more than 6 sides will not tessellate?
The tessellating polygons must meet at a point. At that point, the sum of the interior angles of the polygons must 360 degrees - the sum of angles around any point. Therefore, each interior angle must divide 360 evenly. The interior angles of regular polygons with 7 or more sides lie in the range (120, 180) degrees and so cannot divide 360.
Why will only three of the regular polygons tessellate the plane?
The tessellating polygons must meet at a point. At that point, the sum of the interior angles of the polygons must 360 degrees - the sum of angles around any point. Therefore, each interior angle must divide 360 evenly. There is no 1 or 2 sided polygon. The interior angle of a regular pentagon is 108 degrees which does not divide 360 degrees. The interior angles of regular polygons with 7 or more sides lie in the range (120, 180) degrees and so cannot divide 360.That leaves regular polygons with 3, 4 or 6 sides.
What are concentric polygons?
Anythings that are concentric share the same "center". In this case, regular polygons (mostly) have a point in their interior that is the same distance from each of its vertices ("corners"). Concentric polygons would all have the same center point.
Why is a star polygon concave?
because the point of origin would be on an outer point and around it the walls seem to cave in making it seem concave, in comparison to a regular polygon. When checking for concave polygons always compare what you are looking at to a regular polygon
What is the defenition of a polygon?
A simple closed figure formed by line segments joined together. The point where the sides meet is called the vertex (vertices, plural). A regular polygon is formed when all the sides are equal. Polygons are named by the number of sides and angles they contain.
