# Demicross

n-demicross
Rankn
TypeUniform
SpaceSpherical
Notation
Coxeter diagram.../2 (o3o3/2o3o3*a3o...o3x)
Elements
Vertices2n
Vertex figuren−1-demicross
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt2}{2}}$
Inradius${\displaystyle \frac{1}{\sqrt{2n}}}$ (for simplex facets)
Surface area${\displaystyle \frac{\left(n+\sqrt{n}\right)\sqrt{2^{n-1}}}{\left(n-1\right)!}}$
Dihedral angle${\displaystyle \arccos\left(\frac{1}{\sqrt{n}}\right)}$
Height${\displaystyle \frac{2}{\sqrt{2n}}}$
Related polytopes
ConjugateNone
Abstract & topological properties
Flag count${\displaystyle \left(n-1\right)!\times2^{n-1}\left(n+1\right)}$
OrientableNo
Properties
SymmetryDn, order ${\displaystyle n!\times2^{n-1}}$
ConvexNo
NatureTame

The demicross series is a series of quasiregular, semiregular polytopes. A d-dimensional demicross shares all its vertices, edges, and all elements up to ridges (dimension d-2) with the n-dimensional orthoplex. However, it only uses half of the orthoplex's facets, along with d (d-1)-orthoplexes which pass through the center of the polytope, making all demicrosses hemipolytopes. Its vertex figure is the demicross of the previous dimension.

In all dimensions greater than or equal to 3, the demicross is uniform. A semi-uniform bowtie formed from faceting a square could be considered to be the 2D demicross.

## Examples

Demicrosses by dimension
Rank Name
3 Tetrahemihexahedron
4 Tesseractihemioctachoron
• ${\displaystyle \left(\pm\frac{\sqrt2}{2},\,0,\,0,\,...,\,0\right)}$,