Gripper: Difference between revisions

Gripper
Rank3
TypeOrbiform
Notation
Bowers style acronymGripper
Elements
Faces1+3 triangles, 3 squares, 3 hexagons
Edges3+3+3+6+6
Vertices3+3+6
Vertex figures3 bowties, edge lengths 1 and 3
3 bowtie,s edge lengths 2 and 3
6 scalene triangles, edge lengths 1, 2, 3
Measures (edge length 1)
Dihedral angles3–4: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
3–6: ${\displaystyle \arccos \left({\frac {1}{3}}\right)\approx 70.52878^{\circ }}$
4–6: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Related polytopes
ArmyCo
RegimentGripper
ConjugateNone
Abstract & topological properties
Flag count84
OrientableNo
Properties
SymmetryA2×I, order 6
ConvexNo
NatureTame

The gripper is a nonconvex orbiform polyhedron and an edge faceting of the cuboctahedron. Its faces are 1+3 triangles, 3 squares, and 3 hexagons. It can be constructed by blending either an octahemioctahedron or a cubohemioctahedron with a triangular cupola at a common hexagonal face. In the process the shared hexagon and either 3 triangles or 3 squares, respectively, blend out.

Vertex coordinates

Its vertices are the same as those of the cuboctahedron.