Square scalene

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Square scalene
Rank4
TypeSegmentotope
Notation
Bowers style acronymSquasc
Coxeter diagramxo ox4oo&#x
Tapertopic notation[11]2
Elements
Cells
Faces
Edges1+4+8
Vertices2+4
Vertex figures2 square pyramids, edge length 1
 4 digonal disphenoids, edge lengths 2 (1 base) and 1 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTet–3–tet: 120°
 Squippy–4–squippy: 90°
 Tet–3–squippy: 60°
HeightsPoint atop squippy:
 Dyad atop tet:
 Trig atop inclined trig:
 Dyad atop perp square:
Central density1
Related polytopes
ArmySquasc
RegimentSquasc
DualSquare scalene
ConjugateNone
Abstract & topological properties
Flag count160
Euler characteristic0
OrientableYes
Properties
SymmetryB2×A1×I, order 16
Flag orbits10
ConvexYes
NatureTame

The square scalene (OBSA: squasc), or square pyramidal pyramid, is a CRF segmentochoron (designated K-4.4 on Richard Klitzing's list). It consists of 2 square pyramids and 4 tetrahedra. It can be thought of as a pyramid based on the square pyramid.

Apart from being a point atop square pyramid, it has alternate segmentochoron representations as a dyad atop tetrahedron, dyad atop perpendicular square and triangle atop inclined triangle.

It can be viewed as a quarter of the hexadecachoron or a half of the octahedral pyramid.

Vertex coordinates[edit | edit source]

The vertices of a square scalene with unit edge length are given by:

  • ,
  • ,
  • ,
  • .

It can also be given by the integral coordinates:

  • ,
  • .

Representations[edit | edit source]

The square scalene has the following Coxeter diagrams:

  • xo ox4oo&#x (full symmetry, dyad atop fully orthogonal square)
  • xo ox ox&#x (A1×A1×A1 symmetry, rectangle scalene)
  • oox4ooo&#x (BC2 symmetry, square pyramidal pyramid)
  • oox oox&#x (A1×A1 symmetry, rectangle pyramid pyramid)
  • xoo oxx&#x (A1×A1 symmetry, trapezoid scalene)
  • xoox&#x (bilateral symmetry only)

External links[edit | edit source]