# Heptagonal-hendecagrammic duoprism

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The **heptagonal-hendecagrammic duoprism**, also known as the **7-11/3 duoprism**, is a uniform duoprism that consists of 11 heptagonal prisms and 7 hendecagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the heptagonal-small hendecagrammic duoprism, the heptagonal-great hendecagrammic duoprism, or the heptagonal-grand hendecagrammic duoprism.

## Vertex coordinates[edit | edit source]

The coordinates of a heptagonal-hendecagrammic duoprism, centered at the origin and with edge length 4sin(π/7)sin(3π/11), are given by:

- (2sin(3π/11), 0, 1, 0),
- (2sin(3π/11), 0, 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
- (2sin(3π/11), 0, 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
- (2sin(3π/11), 0, 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
- (2sin(3π/11), 0, 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
- (2sin(3π/11), 0, 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)),
- (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 1, 0),
- (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
- (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
- (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
- (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
- (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)),
- (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 1, 0),
- (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
- (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
- (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
- (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
- (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)),
- (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 1, 0),
- (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
- (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
- (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
- (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
- (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)).

## External links[edit | edit source]

- Bowers, Jonathan. "Category A: Duoprisms".

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