Gripper: Difference between revisions

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{{Infobox polytope
{{Infobox polytope
|type=[[Orbiform]]
|type = [[Orbiform]]
|img=
|img=
|3d=
|3d=
|off=
|off=
|dim = 3
|rank = 3
|obsa = Gripper
|obsa = Gripper
|faces = 1+3 [[triangle]]s, 3 [[square]]s, 3 [[hexagon]]s
|faces = 1+3 [[triangle]]s, 3 [[square]]s, 3 [[hexagon]]s
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|verf2 = 3 [[bowtie]],s edge lengths {{radic|2}} and {{radic|3}}
|verf2 = 3 [[bowtie]],s edge lengths {{radic|2}} and {{radic|3}}
|verf3 = 6 [[scalene triangle]]s, edge lengths 1, {{radic|2}}, {{radic|3}}
|verf3 = 6 [[scalene triangle]]s, edge lengths 1, {{radic|2}}, {{radic|3}}
|army=[[Co]]
|army = [[Co]]
|reg='''Gripper'''
|reg = '''Gripper'''
|symmetry = [[Triangular pyramidal symmetry|A<sub>2</sub>×I]], order 6
|symmetry = [[Triangular pyramidal symmetry|A<sub>2</sub>×I]], order 6
|circum=1
|circum = 1
|dih = 3–4: <math>\arccos\left(-\frac{\sqrt3}{3}\right) \approx 125.26439^\circ</math>
|dih = 3–4: <math>\arccos\left(-\frac{\sqrt3}{3}\right) \approx 125.26439^\circ</math>
|dih2 = 3–6: <math>\arccos\left(\frac13\right) \approx 70.52878^\circ</math>
|dih2 = 3–6: <math>\arccos\left(\frac13\right) \approx 70.52878^\circ</math>
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|dual =
|dual =
|conjugate = None
|conjugate = None
|conv=No
|conv = No
|orientable=No
|orientable = No
|nat=Tame
|nat = Tame
}}
}}
The '''gripper''' is a nonconvex [[orbiform]] polyhedron and an edge faceting of the [[cuboctahedron]]. Its faces are 1+3 [[triangle]]s, 3 [[square]]s, and 3 [[hexagon]]s. 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.
The '''gripper''' is a nonconvex [[orbiform]] polyhedron and an edge faceting of the [[cuboctahedron]]. Its faces are 1+3 [[triangle]]s, 3 [[square]]s, and 3 [[hexagon]]s. 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==
==Vertex coordinates==
Its vertices are the same as those of the [[cuboctahedron]].
Its vertices are the same as {{those of|cuboctahedron}}.


==External links==
==External links==
*{{Bowers|octco|Batch 1: Oct and Co Facetings|5 under co}}
*{{Bowers|octco|Batch 1: Oct and Co Facetings|5 under co}}


{{stub}}
{{acra|6-4-3}}
[[Category:Co army]]
[[Category:Co army]]
[[Category:A2×I symmetry]]
[[Category:A2×I symmetry]]
[[Category:Polyhedra with 10 faces]]
[[Category:Polyhedra with 10 faces]]
[[Category:Facetings of the cuboctahedron]]
[[Category:Facetings of the cuboctahedron]]
{{stub}}

Revision as of 18:02, 11 February 2024

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)
Circumradius1
Dihedral angles3–4:
 3–6:
 4–6:
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.

External links