8demicube
8demicube  

Rank  8 
Type  Uniform 
Notation  
Bowers style acronym  Hocto 
Coxeter diagram  x3o3o3o3o3o3o *b3o () 
Elements  
Zetta 

Exa 

Peta 

Tera 

Cells  1792+8960 tetrahedra 
Faces  7168 triangles 
Edges  1792 
Vertices  128 
Vertex figure  Rectified 7simplex, edge length 1 
Measures (edge length 1)  
Circumradius  1 
Hypervolume  
Dizettal angles  Hesa–hop–oca: 
Hesa–hax–hesa: 90°  
Height  
Central density  1 
Number of external pieces  144 
Level of complexity  6 
Related polytopes  
Army  Hocto 
Regiment  Hocto 
Dual  Semistellated diacosipentacontahexazetton 
Conjugate  None 
Abstract & topological properties  
Flag count  30965760 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  D_{8}, order 5160960 
Flag orbits  6 
Convex  Yes 
Nature  Tame 
The 8demicube, also called the demiocteract, hemiocteract, or hocto, is a convex uniform 8polytope. It has 16 7demicubes and 128 7simplices as facets, with 8 of each at a vertex forming a rectified 7simplex as the vertex figure. It is the 8dimensional demihypercube and is formed by alternating the 8cube. It is also a segmentozetton, as a 7demicubic antiprism.
The 8demicube can also be seen as the convex hull of two opposite hexadecachoric duoprisms, and also contains the vertices of a tetrahedral5demicubic duoprism. A unit 8demicube can be vertexinscribed into the 4_{21} polytope.
Vertex coordinates[edit  edit source]
The vertices of an 8demicube of edge length 1, centered at the origin, are given by all even sign changes of:
 .
Representations[edit  edit source]
An 8demicube has the folowing Coxeter diagrams:
 x3o3o3o3o3o3o *b3o () (full symmetry)
 s4o3o3o3o3o3o3o () (as alternated octeract)
 xo3oo3ox *b3oo3oo3oo3oo&#x (D_{7} axial, 7demicubic antiprism)
 xooo3oooo3oxoo3oooo3ooxo3oooo3ooox&#xt (A_{7} axial, 7simplexfirst)
 ooooo3oxooo3ooooo3ooxoo3ooooo3oooxo3ooooo&#xt (A_{7} axial, vertexfirst)
 xo3oo3ox *b3oo xo3oo3ox *f3oo&#zx (hull of two hexadecachoric duoprisms)
External links[edit  edit source]
 Klitzing, Richard. "hocto".
 Wikipedia contributors. "8demicube".