# Quasitruncated small stellated dodecahedron

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Quasitruncated small stellated dodecahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Quit sissid |

Coxeter diagram | x5/3x5o () |

Elements | |

Faces | 12 pentagons, 12 decagrams |

Edges | 30+60 |

Vertices | 60 |

Vertex figure | Isosceles triangle, edge lengths (1+√5)/2, √(5–√5)/2, √(5–√5)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 10/3–10/3: |

5–10/3: | |

Central density | 9 |

Number of external pieces | 132 |

Level of complexity | 11 |

Related polytopes | |

Army | Srid, edge length |

Regiment | Quit sissid |

Dual | Great pentakis dodecahedron |

Conjugate | Truncated great dodecahedron |

Convex core | Dodecahedron |

Abstract & topological properties | |

Flag count | 360 |

Euler characteristic | –6 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **quasitruncated small stellated dodecahedron**, or **quit sissid**, also called the **small stellated truncated dodecahedron**, is a uniform polyhedron. It consists of 12 pentagons and 12 decagrams. Each vertex joins one pentagon and two decagrams. As the name suggests, it can be obtained by the quasitruncation of the small stellated dodecahedron.

## Vertex coordinates[edit | edit source]

A quasitruncated small stellated dodecahedron of edge length 1 has vertex coordinates given by all permutations of:

together with all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#18).

- Klitzing, Richard. "Quit sissid".
- Wikipedia contributors. "Small stellated truncated dodecahedron".
- McCooey, David. "Small Stellated Truncated Dodecahedron"