Posts tagged: geometry

This truncation shows that the dual polyhedron of the tetrahedron is itself.
More here.

(via ultrazapping)

This truncation shows that the dual polyhedron of the tetrahedron is itself.


More here.

(via ultrazapping)




This is what it would look like to spin around in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.




This is what it would look like to do a front flip in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.




Flying though a tiling of regular right angled dodecahedron in three dimensional hyperbolic space. There is more of an explanation here.

Created with Curved Spaces.


The lemniscate can be generated as the envelope of circles centered on a rectangular  hyperbola and passing through the center of the hyperbola.

The lemniscate can be generated as the envelope of circles centered on a rectangular hyperbola and passing through the center of the hyperbola.

An arbitrary point P on a torus (not lying in the xy-plane) can have four circles drawn through it. The first circle is in the plane of the torus and the second is perpendicular to it. The third and fourth circles are called Villarceau circles.

This truncation shows that the dodecahedron and the icosahedron are dual polyhedra.See here for another example with the cube and octahedron.

(via geometryofdopeness)


This truncation shows that the dodecahedron and the icosahedron are dual polyhedra.

See here for another example with the cube and octahedron.

(via geometryofdopeness)

(via thepatterns)


(via thepatterns)

enkiseshat:

Just as a cube can be unfolded into 2-D as 6 squares, a tesseract can be unfolded into 3-D as 6 cubes.

enkiseshat:

Just as a cube can be unfolded into 2-D as 6 squares, a tesseract can be unfolded into 3-D as 6 cubes.

An ideal rotation around the point at infinity in the disc and upper half plane model of the hyperbolic plane







Rotation around the symmetry axis of 4th order in the disk and upper half plane models