Search
Subject Categories:
 Art (462)
 Asperger's (32)
 Blogging (11)
 China and the Han (9)
 eBay (3)
 Education (93)
 Fiction (29)
 Geography (27)
 History (38)
 Humor (49)
 Life (363)
 Mandalas (126)
 Mathematics (1,275)
 Mental Health (74)
 Music (43)
 Mysteries (16)
 Politics (121)
 Quotations (64)
 Religion (58)
 Satire (12)
 Science and Scientists (121)
 Follow RobertLovesPi.net on WordPress.com
MostViewed Posts, Recently:

Recent Posts
 Octahedra and Cuboctahedra Can Fill Space Without Leaving Any Gaps
 Spectral Circles #3
 A Compound of the Great Stellated Dodecahedron and the Great Dodecahedron
 One Dozen Icosahedra
 Tessellation of Rhombi and Tetraconcave Octagons
 A Radial Tessellation Using Three Types of Rhombi
 A Radial Tessellation Using Two Types of Rhombi
 A Zonohedron with 1382 Faces, Based on the Rhombicosidodecahedron
 Spectral Circles #2
 Four Different Faceted Versions of the Rhombicosidodecahedron
Explore RobertLovesPi By Topic
 Arkansas
 Art
 Asperger's
 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
 rhombi
 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
 355,155 hits
Tag Archives: convex hull
The Compound of the Truncated Isocahedron and the Pentakis Dodecahedron, with Related Polyhedra
The yellowandred polyhedron in the compound below is the truncated icosahedron, one of the Archimedean solids. The blue figure is its dual, the pentakis dodecahedron, which is one of the Catalan solids. The next image shows the convex hull of … Continue reading
Posted in Mathematics
Tagged compound, convex hull, dual, geometry, Mathematics, pentakis dodecahedron, polyhedra, polyhedron, truncated icosahedron
Leave a comment
Eight KiteRhombus Solids, Plus Five AllKite Polyhedra — the Convex Hulls of the Thirteen ArchimedeanCatalan Compounds
In a kiterhombus solid, or KRS, all faces are either kites or rhombi, and there are at least some of both of these quadrilateraltypes as faces. I have found eight such polyhedra, all of which are formed by creating the … Continue reading
Posted in Mathematics
Tagged Archimedean, Catalan, convex hull, dual, duality, geometry, kite, Mathematics, polyehdron, polyhedra, rhombi, rhombus, solid
Leave a comment
ThirtyFour Rotating, Convex, and NonChiral Polyhedra with Icosidodecahedral Symmetry
Most in the field call this type of symmetry “icosahedral,” but I prefer the term George Hart uses — along with “cuboctahedral” in place of “octahedral.” Each polyhedral image here was created with Stella 4d: Polyhedron Navigator. At this linked … Continue reading
Posted in Mathematics
Tagged convex hull, geometry, icosahedral symmetry, icosidodecahedral symmetry, Mathematics, polyhedra, polyhedron
2 Comments
A Polyhedral Journey, Beginning with the Snub Cube / Pentagonal Isositetrahedron Base/Dual Compound
The snub cube and its dual make an attractive compound. Since the snub cube is chiral, its chirality is preserved in this compound. If you examine the convex hull of this compound, you will find it to be chiral as … Continue reading
Posted in Mathematics
Tagged chiral, chirality, compound, convex hull, dual, geometry, Mathematics, pentagonal icositetrahedron, polyhedra, polyhedron, snub cube, stellate, stellation
Leave a comment
A Collection of Unusual Polyhedra
In the post directly before this one, the third image was an icosahedral cluster of icosahedra. Curious about what its convex hull would look like, I made it, and thereby saw the first polyhedron I have encountered which has 68 … Continue reading
Posted in Mathematics
Tagged convex hull, dual, geometry, Mathematics, polyhedra, polyhedron, stellate, stellation
Leave a comment
A Polyhedral Investigation, Starting with an Augmentation of the Truncated Octahedron
If one starts with a central truncated octahedron, leaves its six square faces untouched, and augments its eight hexagonal faces with trianglular cupolae, this is the result. Seeing this, I did a quick check of its dual, and found it … Continue reading
Posted in Mathematics
Tagged augment, augmentation, convex hull, cupola, dual, truncated octahedron
2 Comments