#polytope

[ketrinadrawsalot]

The Octochoron answers to many names--Tesseract, Hypercube, 8-Cell, and Free Hugs. She will happily receive hugs as well as give them.

[rauko]

Calabi-Yau Manifold E8 Gosset Lattice

laser etched glass | 80x80mm

[ll-madame-minty-chip-ll]

Random ass doodles

Feat:

Eins(My oc)

Rax(My oc)

Borareta(DBS)

Rabanra(DBS)

Pikmin(Red)

Mystic Flour(CRK)

Coqroc polytope

Unit Circle

Trigonometry

Gamma Function

Epsilon Naught

Protractor

Pukeko(DAMMMMMNNNNNNN meme)

Lollipop(Dum Dums)

[dragonpride17]

polyhedral (link) terminology!

polyhedrity - the noun form of polyhedral

vanadinitian - polyhedral loving polyhedral (plLpl)

jupexian - a galactian alignment term for those who are polyhedral-aligned

hedramel / hedranox / hedranon - a sex categorization title for those who are polyhedral

prism - a polyhedral individual, regardless of age

verti - a younger polyhedral individual (plural form: verties)

isometran - an older polyhedral individual (plural form: isometren)

polytope - a presentation term for someone who presents in a polyhedral way, or whose presentation can only be described as polyhedral

phylla- - a prefix for those who have a connection to polyhedrity, either in gender or expression

@daybreakthing @neoumbrellatime @radiomogai

[knotty-et-al]

Polytope info card of the Truncated Cuboctahedron

Today I finished this friend-shaped archimedian solid.

I drew the tiny drawing in the down right corner of the card and resized it with my printer.

The drawing:

I drew this Truncated cuboctahedron in an isometric projection and used my beloved isometric dot paper.

To start with the truncated cuboctahedron I started to draw a cube (with pencil).

Then I altered the cube by drawing a cuboctahedron in it (with pencil as well). I truncated th vertices of the cube like in the depiction below:

Then I altered the cuboctahedron drawing with another truncation - resulting in the truncated cuboctahedron shape.

[For clarification: I later erased the pencil lines of the cube and cuboctahedron, because it became messy and these lines were just there to help in the drawing process.

For the photo I laid pictures of a cube and cuboctahedron besides the truncated cuboctahedron drawing to show the similarity between these shapes - and present the principle of truncation visually.)

[noosphe-re]

Tribe - A continuous set of semi-uniform polytopes (or compounds) that span several teepees. Truncation rotation is an example with one variable of morphing. Wythoffian cases will include all polytopes with a particular symbol (example xy^z) allowing the variables (x,y,z, etc) to take on any value including negative. The following pic displays the grid tribe (which contains 4 clans and 60 teepees). Each teepee is displayed twice on the pic with an example polyhedron within a triangle shaped region (the sides of the dual of grid). The grid tribe's clans are xy^z (grid), x,y^z (reboga), xy^'z (badori), and x,y^'z (robisu) - where x,y,and z take on positive values. There are 11 spitsu tribes under grid, they are xy^z (grid, 60 teepees), x*y^z (quitdid, 60 teepees), xy*z (gaquatid, 60 teepees), (x^y*'z) (idtid, 60 teepees), (xy*z) (becada, 30 teepees), (x^y^z,) (fabeca, 30 teepees), (xy^'z) (cafeta, 30 teepees), (x*y*z,) (mocaba, 30 teepees), (x^'y^'z^') (jefari, 10 teepees), (x*y*z*) (vamesa, 10 teepees), and the 15-block compound tribe x y z (broza, 5 teepees). I suspect that four dimensional tribes, such as the gidpixhi tribe could have as many as 7200 teepees with three variables of morphing. (source)

[theinquisitivereceptacle]

A collection of uniform polychora and other four dimensional objects from www.polytope.net  Explore here: http://www.polytope.net/hedrondude/polychora.htm#categories

[numb3rth30ry]

An order 4 permutohedron.

Quoting Wikipedia, “In mathematics, the permutohedron of order n (also spelled permutahedron) is an (n − 1)-dimensional polytope embedded in an n-dimensional space, the vertices of which are formed by permuting the coordinates of the vector (1, 2, 3, ..., n). More generally, the term describes any polyhedron which is the convex hull of a free orbit of the symmetric group Sn acting naturally on R^n. The edge-graph of any permutohedron is the Cayley graph of Sn with respect to the generating set of adjacent transpositions (1,2), . . . , (n − 1,n).”

Mathematics is beautiful. <3