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Which polygons do not tessellate?
Pentagons, decagons, and octagons will not tessellate. In order to create a tessellation, the sum of the angles at a point must be 360.
Why can any shape tessellate?
Not all shapes can tessellate. For example a pentagon will not tessellate. Only those shapes where the angles of the vertices which meet sum to 360° (a full turn) will tessellate. For example, with a regular hexagon, each angle is 120° and when three come together they form 3×120° = 360° and so will tessellate, but with an octagon, each angle is 135°; two such angles form 2×135° = 270°, but three such angles form 3×135° = 405° - two octagons will lay together with a gap, but three octagons will overlap: they cannot tessellate; however, 360° - 270° = 90° which is the angle of a square, so octagons together with squares will tessellate.
How do you create a quilt only using geometric shapes?
Select a shape that tessellates. Some shapes will tessellate by themselves, others will tessellate in pairs (octagons and squares), or larger groups. See the link for a flavour.
Describe a combination of a regular octagon and another regular polygon that will tessellate the plane?
A regular octagon can tessellate the plane when combined with regular squares. By placing a square in the center of the octagon and surrounding it with eight octagons, the shapes can be repeated infinitely, filling the plane without gaps or overlaps
How many perpendicular lines do octagons have?
Octagons have no perpendicular lines.
Can octagons tessellate?
no
Do octagons tessellate?
No it does not tessellate you have to pentagons in order for it to tessellate. * * * * * It is not at all clear what "have to pentagons" has to do with this. No polygon with 7 or more sides will tessellate. Octagons will tessellate if mixed with squares but that is not "proper" tessellation since it involved more than one shape.
The addition of what shape will allow regular octagons to tessellate?
Squares.
Why wont octagons tessellate?
Their inner angles are not a multiple of 360 degrees.
Which polygons do not tessellate?
Pentagons, decagons, and octagons will not tessellate. In order to create a tessellation, the sum of the angles at a point must be 360.
What is one type of tessellation?
Triangles, squares, hexagons, and octagons all tessellate
Can an octagon and square tessellate?
Yes - because, when you lay regular octagons together so they're touching, the space between the octagons is a perfect square.
Why can any shape tessellate?
Not all shapes can tessellate. For example a pentagon will not tessellate. Only those shapes where the angles of the vertices which meet sum to 360° (a full turn) will tessellate. For example, with a regular hexagon, each angle is 120° and when three come together they form 3×120° = 360° and so will tessellate, but with an octagon, each angle is 135°; two such angles form 2×135° = 270°, but three such angles form 3×135° = 405° - two octagons will lay together with a gap, but three octagons will overlap: they cannot tessellate; however, 360° - 270° = 90° which is the angle of a square, so octagons together with squares will tessellate.
How do you create a quilt only using geometric shapes?
Select a shape that tessellates. Some shapes will tessellate by themselves, others will tessellate in pairs (octagons and squares), or larger groups. See the link for a flavour.
Can a regular octagon be tessellated?
no it cant be unless you use pentagons and octagons like on a soccer ball * * * * * That is an unbelievably rubbish answer! Tessellation - unless otherwise specified - refers to covering a 2-d surface, not the surface of a sphere. Normal soccer balls do not have pentagons and octagons but pentagons and hexagons.
Why can't a regular octagon tessellate?
To be able to tessellate where a vertex meets other vertices, the total of those angles must be a full circle of 360°. The interior angle of an Octagon is 135° which does not divide into 360° which means there cannot be a complete number of vertices meeting and so it cannot, by itself, tessellate. However, two octagons meeting at a point would have 135° + 135° = 270° leaving 90° which is the interior angle of a square. So octagons and squares together will tessellate.
Describe a combination of a regular octagon and another regular polygon that will tessellate the plane?
A regular octagon can tessellate the plane when combined with regular squares. By placing a square in the center of the octagon and surrounding it with eight octagons, the shapes can be repeated infinitely, filling the plane without gaps or overlaps
