Visual geometry, geometric drawings ,
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Squares and pentagons |
Extended lines of regular polygons.
Looking at the first intersection of the lines extending from regular polygons which has the shape of a geometric star.
The polygons are arranged in a circle and the pattern repeated all around.
Vesica piscis and regular polygons.
All the vesica piscis in those regular polygons are 4 regular polygons short of a full circle (Odd sided polygons) . In a triange for example the vesica piscis has two triangles , when a full circle would have 6. In a pentagon the vesica has 6 pentagons when the full circle has 10.
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Triangle |
Hexagon dissections and the 6n+3 series
I found the inspiration for this ones looking at https://people.missouristate.edu/LesReid/HS175.html , which can also be found at :
https://en.m.wikipedia.org/wiki/File:Equilateral_pentagonal_dissection_of_regular_octadecagon.svg
which is a pentagonal dissection of a 18-gon.
I made this one with a hexagon at the centre and adding nonagons from the radius lines. I then use parallel lines to find the rest of the points needed to complete the drawing.
The following hexagonal dissections/tessellations are made using the nonagon (9-gon) , 15-gon and 21-gon ( 6n+3 series).
Regular polygons with odd numbers.
Looking at the diagonals of regular polygons, in this case odd number regular polygons.
Today I'm looking at the 3 smaller regular polygons that can be constructed radiating from the centre, that can be encased with another bigger regular polygon .Diagonal lines and circles are used to find defining points.