# Pentagonal antiprismatic symmetry

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### Convex polytopes with (G

Pentagonal antiprismatic symmetry | |
---|---|

Rank | 3 |

Space | Spherical |

Order | 20 |

**Pentagonal antiprismatic symmetry**, also known as **pappic symmetry** and notated **(I _{2}(10)×A_{1})/2**, is a 3D spherical symmetry group. It is the symmetry group of the pentagonal antiprism and is a subgroup of icosahedral symmetry.

### Subgroups[edit | edit source]

- (I
_{2}(10)+×A_{1})/2 (maximal) - (H
_{2}×A_{1})+ (maximal) - H
_{2}×I (maximal) - H
_{2}+×I - K
_{2}+×A_{1}(maximal) - K
_{2}+×I - ±(I×I×I)
- A
_{1}×I×I - I×I×I

### Convex polytopes with (G_{2}×A_{1})/2 symmetry[edit | edit source]

- Pentagonal antiprism (isogonal)/Pentagonal antitegum (isotopic)
- Dipentagonal trapezoprism (isogonal)/Pentagonal scalenohedron (isotopic)