Enneagonal antiprism

In geometry, the enneagonal antiprism (or nonagonal antiprism) is one in an infinite set of convex antiprisms formed by triangle sides and two regular polygon caps, in this case two enneagons.

Uniform enneagonal antiprism
TypePrismatic uniform polyhedron
ElementsF = 20, E = 36
V = 18 (χ = 2)
Faces by sides18{3}+2{9}
Schläfli symbols{2,18}
sr{2,9}
Wythoff symbol| 2 2 9
Coxeter diagram
Symmetry groupD9d, [2+,18], (2*9), order 36
Rotation groupD9, [9,2]+, (922), order 18
ReferencesU77(g)
DualEnneagonal trapezohedron
Propertiesconvex

Vertex figure
3.3.3.9

Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals.

In the case of a regular 9-sided base, one usually considers the case where its copy is twisted by an angle 180°/n. Extra regularity is obtained by the line connecting the base centers being perpendicular to the base planes, making it a right antiprism. As faces, it has the two n-gonal bases and, connecting those bases, 2n isosceles triangles.

If faces are all regular, it is a semiregular polyhedron.

See also

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