# Biambodecachoron

Biambodecachoron Rank4
TypeIsogonal
SpaceSpherical
Notation
Bowers style acronymBamid
Coxeter diagramoo3xo3ox3oo&#zy
Elements
Cells10 tetrahedra, 20 triangular antiprisms
Faces40 triangles, 60 isosceles triangles
Edges30+60
Vertices20
Vertex figureTriangular bifrustum
Measures (based on two rectified pentachora of edge length 1)
Edge lengthsLacing edges (30): $\frac{\sqrt{10}}{5} ≈ 0.63246$ Edges of rectified pentachora (60): 1
Circumradius$\frac{\sqrt{15}}{5} ≈ 0.77460$ Central density1
Related polytopes
ArmyBamid
RegimentBamid
DualBijungatodecachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA4×2, order 240
ConvexYes
NatureTame

The biambodecachoron or antiprismatodecachoron, short name bamid or apid, is a convex isogonal polychoron that consists of 10 tetrahedra and 20 triangular antiprisms. 2 tetrahedra and 6 triangular antiprisms join at each vertex. It can be obtained as the convex hull of two oppositely oriented rectified pentachora. Alternatively it can be obtained as the hull of the centers of the triangular faces of the decachoron.

It is also one of a number of polychora obtained as the hull of 2 10-3 step prisms.

The ratio between the longest and shortest edges is 1:$\frac{\sqrt{10}}{2}$ ≈ 1:1.58114.

## Vertex coordinates

Coordinates for the vertices of a biambodecachoron, based on two rectified pentachora of edge length 1, centered at the origin, are given by:

• $±\left(-\frac{3\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,0,\,0\right),$ • $±\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0\right),$ • $±\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12\right),$ • $±\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{\sqrt3}{3},\,0\right),$ • $±\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{\sqrt3}{3},\,0\right),$ • $±\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,±\frac12\right),$ • $±\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,±\frac12\right).$ 