Parabolic sector

Parabolic sector
Dimensionality	2
Subfacets
Vertices	2 points
Edges	1 line segment 1 parabolic segment
Faces	1 parabolic sector
Hypervolumes
Vertex Count	'"`UNIQ--postMath-00000001-QINU`"'
Edge Length	'"`UNIQ--postMath-00000002-QINU`"'
Surface Area	'"`UNIQ--postMath-00000003-QINU`"'

A parabolic sector is a 2-dimensional shape bound by a segment of a parabola and a line segment that joins the two vertices called a latus rectum.

Structure and Sections

Hypervolumes

• vertex count = $2$
• edge length = $\sqrt{a^2 + 4h^2} + 2a + \frac{a^2}{2h} \sinh^{-1} \left( \frac{2h}{a} \right)$
• surface area = $\frac {4}{3}ah$

Subfacets

• 2 points (0D)
• 1 line segment (1D)
• 1 parabolic segment (1D)
• 1 parabolic sector (2D)