Six.
Six.
Six.
Six.
Six.
Shapes tessellate to fit around an interior angle. They also tessellate because they are regular polygons; non-regular polygons cannot tessellate. * * * * * Not correct. All triangles and quadrilaterals will tessellate, whether regular or irregular. Contrary to the above answer, a regular pentagon will not tessellate but there are 14 different irregular pentagons which will tessellate (the last was discovered in 2015). Three convex hexagons will do so as well. No polygon of 7 or more sides will tessellate - whether they are regular (contrary to the above answer) or irregular.
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.
When a regular polygon can tessellate, it can be placed around a point (which has an angle of 360 degrees) with no 'space' left over. However some regular polygons don't tessellate because their interior angle is not a factor of 360 (does not go into 360 equally), meaning that there will be 'space' left over or it will overlap. To check if a regular polygon can tessellate, see if it's interior angle goes into 360 equally. (360/interior angle), if it does, it will tessellate and if it doesn't it's because the interior angle is not a factor of 360 meaning it will not fit round a point and won't tessellate.
6 (triangles).
Yes because each interior angle is 120 degrees and angles around a point add up to 360 degrees
Because their angles are factors of 360 and angles around a point add up to 360 degrees
regular distribution of and object around a central axis
If there is a picture with 3 triangles and 1 upside down the the answer to that is OBVIOUSLY 5. Lol. The 4 triangles and the triangle going around the outside of the other little triangles inside of the picture.
Non-regular tessellations is a tessellation in which there is no restriction on the order of the polygons around vertices. There is an infinite number of such tessellations. These are tessellations with nonregular simple convex or concave polygons. All triangles and quadrilaterals will tessellate. Some pentagons and hexagons will.
Yes, they tessellate with squares and hexagons. For every dodecagon , there are 6 squares and 6 hexagons to go around it. They tessellate because every = exterior angle on a dodecagon = 150 degrees . every interior for a hexagon - 120 degrees . every interior for a square - 90 degrees. This adds up to 360 at a point and this is why they tessellate perfectly
Have a look around you?
Equilateral triangles can tile a plane, but regular heptagons cannot; nor can they tile the plan together. Where vertices meet (at a point on the plane) there is a complete turn of 360°. Each vertex of an equilateral triangle is 60°; 360° ÷ 60° = 6, a whole number of times, so a whole number of equilateral triangles can meet at a vertex of the tiling. Each vertex of a regular heptagon is 128 4/7°; 360° ÷ 128 4/7° = 2 4/5 which is not a whole number, so a whole number of regular heptagons cannot meet at a vertex of the tiling, so there will be gaps. With one regular heptagon there are 360° - 128 4/7° = 232 3/7°, but this cannot be divided by 60° a whole number of times, so one regular heptagon and some equilateral triangles cannot meet at a vertex of the tiling without gaps. With two regular heptagons there are 360° - 2 x 128 4/7° = 102 6/7°, but this cannot be divided by 60° a whole number of times, so two regular heptagons and some equilateral triangles cannot meet at a vertex of the tiling without gaps. With three or more regular heptagons, they will overlap when trying to place them on a plane around a point - leaving no space for any equilateral triangles.