Rectangular frustum

Rectangular frustum
Rank3
Notation
Bowers style acronymRectif
Coxeter diagramab cd&#e
Elements
Faces1+1 rectangles, 2+2 isosceles trapezoids
Edges2+2+2+2+4
Vertices4+4
Vertex figureScalene triangle
Measures (edge length 1)
Central density1
Related polytopes
DualDigonal scalenohedron
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA1×A1×I, order 4
ConvexYes
NatureTame

The rectangular frustum or rectif is a variant of the cube with digonal pyramidal symmetry. It has 2 opposite rectangles of different sizes as bases connected by 2+2 isosceles trapezoids in 2 pairs.

In vertex figures

A rectangular frustum with one base a square of edge length 1, the other base a rectangle with edge lengths ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$ and ${\displaystyle {\frac {1+{\sqrt {5}}}{2}}}$, and lacing edges of length ${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{2}}}}$ occurs as the vertex figure of the antifrustary hexacositrishecatonicosachoron.