Search
Subject Categories:
 Art (449)
 Asperger's (32)
 Blogging (9)
 China and the Han (9)
 eBay (3)
 Education (91)
 Fiction (28)
 Geography (27)
 History (37)
 Humor (46)
 Life (358)
 Mandalas (122)
 Mathematics (1,223)
 Mental Health (72)
 Music (43)
 Mysteries (16)
 Politics (120)
 Quotations (64)
 Religion (58)
 Satire (10)
 Science and Scientists (120)
 Follow RobertLovesPi.net on WordPress.com
MostViewed Posts, Recently:

Recent Posts
Explore RobertLovesPi By Topic
 Arkansas
 Art
 Asperger's
 Aspie
 astronomy
 atheism
 atheist
 chemistry
 chiral
 circle
 cluster
 compound
 cube
 cuboctahedron
 dodecahedron
 dual
 Education
 enneagon
 faceted
 faceting
 geometric
 geometrical
 geometrical art
 geometry
 Golden Ratio
 hexagon
 Humor
 humour
 icosahedron
 icosidodecahedral
 icosidodecahedron
 kite
 life
 mandala
 mandalas
 math
 mathematical
 mathematical art
 Mathematics
 music
 nonagon
 octagon
 octahedron
 op art
 pentagon
 physics
 politics
 polygon
 polyhedra
 polyhedral
 polyhedron
 president
 quotation
 quote
 religion
 rhombic dodecahedron
 rhombicosidodecahedron
 rhombic triacontahedron
 rhombus
 school
 science
 snub dodecahedron
 star
 stellated
 stellation
 symmetry
 tessellation
 tetrahedron
 tiling
 triangle
 Trump
 truncated icosahedron
 USA
 words
 zonohedron
Hit Counter
 312,140 hits
Monthly Archives: March 2014
On Classification of Concave Polygons By Number of Concavities
Concave triangles do not exist, so concavity does not appear in the examination of polygons by ascending side length until the quadrilateral. A quadrilateral may only have one concavity, as shown in the red figure. Any polygon with exactly one … Continue reading
A Tessellation Featuring Regular Heptagons
Regular heptagons, of course, can’t tile a plane by themselves. Of all tessellations of the plane which include regular heptagons, I think this is the one which minimizes betweenheptagon gapsize (the parts of the plane outside any heptagon). However, I do not … Continue reading
An Icosahedron Variant Featuring KiteStars
This variant of the icosahedron has five kites meeting at each of its twelve vertices, forming what I call the twelve “kitestars” of this polyhedron. Also, two kites meet at the midpoint of each of the icosahedron’s thirty edges. The … Continue reading
A Variant of Kepler’s Stella Octangula
Johannes Kepler named the compound of two tetrahedra the “stella octangula,” thus helping make it one of the bestknown polyhedral compounds today. This variant uses triakis tetrahedra in place of the Platonic tetrahedra in that compound. The triakis tetrahedron is … Continue reading
The Compound of Six Dodecahedra
Some polyhedral compounds are wellknown, such as the compound of five cubes, while others are less famous. I had never heard of this compound before building one today (virtually, not as a physical model). However, a quick Googlesearch told me that … Continue reading
Image
30 March 2014
Tagged 6, compound, dodecahedra, dodecahedron, geometry, math, Mathematics, polyhedra, polyhedral, polyhedron, six
Leave a comment
Long, Narrow, Multicolored Hexagons As the Edges of a Rotating, Hollow Rhombic Dodecahedron
Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.
A ClosePacking of Space, Using Three Different Polyhedra
This is like a tessellation, but in three dimensions, rather than two. The pattern can be repeated to fill all of space, using cubes (yellow), truncated octahedra (blue), and great rhombcuboctahedra, also known as truncated cuboctahedra (red). Software credit: see … Continue reading