# Gripper: Difference between revisions

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{{Infobox polytope |
{{Infobox polytope |
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|type=[[Orbiform]] |
|type = [[Orbiform]] |
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|img= |
|img= |
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|3d= |
|3d= |
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|off= |
|off= |
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| |
|rank = 3 |
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|obsa = Gripper |
|obsa = Gripper |
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|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}} |
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|verf3 = 6 [[scalene triangle]]s, edge lengths 1, {{radic|2}}, {{radic|3}} |
|verf3 = 6 [[scalene triangle]]s, edge lengths 1, {{radic|2}}, {{radic|3}} |
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|army=[[Co]] |
|army = [[Co]] |
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|reg='''Gripper''' |
|reg = '''Gripper''' |
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|symmetry = [[Triangular pyramidal symmetry|A<sub>2</sub>×I]], order 6 |
|symmetry = [[Triangular pyramidal symmetry|A<sub>2</sub>×I]], order 6 |
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|circum=1 |
|circum = 1 |
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|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> |
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|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 = |
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|conjugate = None |
|conjugate = None |
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|conv=No |
|conv = No |
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|orientable=No |
|orientable = No |
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|nat=Tame |
|nat = Tame |
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}} |
}} |
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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. |
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==Vertex coordinates== |
==Vertex coordinates== |
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Its vertices are the same as those of |
Its vertices are the same as {{those of|cuboctahedron}}. |
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==External links== |
==External links== |
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*{{Bowers|octco|Batch 1: Oct and Co Facetings|5 under co}} |
*{{Bowers|octco|Batch 1: Oct and Co Facetings|5 under co}} |
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⚫ | |||

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

## Revision as of 18:02, 11 February 2024

Gripper | |
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Rank | 3 |

Type | Orbiform |

Notation | |

Bowers style acronym | Gripper |

Elements | |

Faces | 1+3 triangles, 3 squares, 3 hexagons |

Edges | 3+3+3+6+6 |

Vertices | 3+3+6 |

Vertex figures | 3 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) | |

Circumradius | 1 |

Dihedral angles | 3–4: |

3–6: | |

4–6: | |

Related polytopes | |

Army | Co |

Regiment | Gripper |

Conjugate | None |

Abstract & topological properties | |

Flag count | 84 |

Orientable | No |

Properties | |

Symmetry | A_{2}×I, order 6 |

Convex | No |

Nature | Tame |

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

- Bowers, Jonathan. "Batch 1: Oct and Co Facetings" (#5 under co).

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