**Enneagonal and Hendecagonal Near Misses**

Near-miss polyhedra, convex or otherwise, which contain enneagonal (and in the last example) hendecagonal faces.

These polyhedra are also presented as
'**Stress Maps**', a bespoke form of VRML model for showing distortion in such
models. More information on Stress Maps and distortion statistics is available here.

This convex "enneagonal
polyhedron" with octahedral symmetry is a Johnson Solid Near
Miss. It
has perfectly regular enneagons in the face planes of an octahedron, the
squares are also regular but have a side length of only 0.96, this makes
the triangles slightly isosceles. (combo), (stress
map). Distortion (**E**=1.19,
**P**=1.68, **A**=159°). Discoverer: Unknown.

**9-9-3 Acrohedron**

The above polyhedron with icosahedral symmetry
contains examples of the unsolved 9-9-3 acron (see 'acrohedra').
Most of the distortion is contained in the diagonals of the enneagons. Stress
Map. Distortion (**E**=0.119,
**P**=2.63, **A**=431°). Discoverer: Ulrich
Mikloweit 2006.

As something of an aside, above are two facetings of Ulrich's 9-9-3 near miss acrohedron. The left image shows a rhombified faceting containing enneagrams {9/2}, pentagrams and square faces. The right image shows a rhombified faceting containing great-enneagrams {9/4}, pentagons and square faces.

**9-6-3 Acrohedron**

The above polyhedron with tetrahedral symmetry
contains examples of the unsolved 9-6-3 acron (see 'acrohedra').
The enneagons are regular, but the triangle-hexagon edge lengths are around
1.13. Stress Map.
Distortion (**E**=1.65,
**P**=3.44, **A**=223°). Discoverer: Robert
Webb 2006.

**9-3-5-3 Acrohedron**

The above convex polyhedron with icosahedral
symmetry contains examples of the unsolved 9-9-3 and 9-3-5-3 acrons (see 'acrohedra').
The enneagons are regular, but the pentagon edge lengths are around 1.2, making
it a rather 'far miss'. Stress Map. Distortion (**E**=12.1,
**P**=18.6, **A**=1657°). Discoverer: Robert
Webb 2006.

**Hendecagonal Polyhedron**

In similar fashion to the top polyhedron on this page, this "hendecagonal
polyhedron" is based on the snub
cuboctahedron. None of the polygons in the model are not quite regular,
(combo), (stress map).
Distortion (**E**=0.046, **P**=2.08,
**A**=105°). Thanks to Craig Kaplan
for bringing this to my attention. Craig has a page containing this and
similar polyhedra at http://www.cgl.uwaterloo.ca/~csk/projects/nearmisses/

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