Pentagonal-hexagonal duoantiprism

From Polytope Wiki
(Redirected from 5-6 duoantiprism)
Jump to navigation Jump to search
Pentagonal-hexagonal duoantiprism
200px
Rank4
TypeIsogonal
SpaceSpherical
Bowers style acronymPhiddap
Info
Coxeter diagrams10o2s12o
SymmetryI2(10)×I2(12)/2, order 240
ArmyPhiddap
RegimentPhiddap
Elements
Vertex figureGyrobifastigium
Cells60 digonal disphenoids, 12 pentagonal antiprisms, 10 hexagonal antiprisms
Faces120+120 isosceles triangles, 12 pentagons, 10 hexagons
Edges60+60+120
Vertices60
Measures (based on polygons of edge length 1)
Edge lengthsLacing (120):
 Edges of pentagons (60): 1
 Edges of hexagons (60): 1
Circumradius
Central density1
Euler characteristic0
Related polytopes
DualPentagonal-hexagonal duoantitegum
Properties
ConvexYes
OrientableYes
NatureTame

The pentagonal-hexagonal duoantiprism or phiddap, also known as the 5-6 duoantiprism, is a convex isogonal polychoron that consists of 10 hexagonal antiprisms, 12 pentagonal antiprisms, and 60 digonal disphenoids. 2 hexagonal antiprisms, 2 pentagonal antiprisms, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the decagonal-dodecagonal duoprism. However, it cannot be made uniform, as it generally has 3 edge lengths, which can be minimized to no fewer than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.35539.

Vertex coordinates[edit | edit source]

The vertices of a pentagonal-hexagonal duoantiprism based on pentagons and hexagons of edge length 1, centered at the origin, are given by: