The tetracontaoctagon appeared in Archimedes'polygon approximation of pi, along with the hexagon ( 6-gon ), dodecagon ( 12-gon ), icositetragon ( 24-gon ), and enneacontahexagon ( 96-gon ).
32.
The enneacontahexagon appeared in Archimedes'polygon approximation of pi, along with the hexagon ( 6-gon ), dodecagon ( 12-gon ), icositetragon ( 24-gon ), and tetracontaoctagon ( 48-gon ).
33.
In 3-dimensions it will be a zig-zag skew dodecagon and can be seen in the vertices and side edges of a hexagonal antiprism with the same D 5d, [ 2 +, 10 ] symmetry, order 20.
34.
The Nauru graph can also be constructed as the generalized Petersen graph " G " ( 12, 5 ) which is formed by the vertices of a dodecagon connected to the vertices of a twelve-point star in which each point of the star is connected to the points five steps away from it.
35.
Nine ideal centrally-planned geometrical shapes are recommended for churches; besides the circle he lists the square, the hexagon, octagon, decagon and dodecagon, all derived from the circle, and, derived from the square, rectangles that exhibit the square and a half, square and a third and double square, all of which have enharmonic parallels in music.
36.
About Davis'paintings of the late 1960s in an essay accompanying the Ronald Davis retrospective exhibition " Forty Years of Abstraction, " at the Butler Institute of American Art in 2002, the abstract painter Ronnie Landfield wrote : " the Dodecagons from 1968 69 remain among the most visually stunning, audacious and intellectually interesting bodies of work made by an abstract painter in the last half of the twentieth century ."
37.
:" " Multiply one side of a hexagon by the radius ( of its circumcircle ), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the finer we cut, the smaller the loss with respect to the area of circle, thus with further cut after cut, the area of the resulting polygon will coincide and become one with the circle; there will be no loss " ".
38.
:" " Multiply one side of a hexagon by the radius ( of its circumcircle ), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the finer we cut, the smaller the loss with respect to the area of circle, thus with further cut after cut, the area of the resulting polygon will coincide and become one with the circle; there will be no loss " ".
