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 Innovation and Technology for Mathematics Education

ATCM 2014 Art Gallery

This page is almost an exact copy of a web page from the web site of my friend Dr Tadeusz Doroziński. Tadeusz i a Polish mathematician with perticular interest in 3D geometry. His works use unique techniques and specific algorithms designed by Tadeusz. He lives in Germany and his web site can be found at http://www.3doro.de/ . All graphics on ATCM 2014 pages are displayed with his permission.

Mirek Majewski, 21/11/2014

## Operations on regular polyhedra

The three operations modify regular polyhedra a following way:

• Blunting (cutting corners) - denoted by t (truncation ),
• Center-numbing - denoted by m (midpoint )
• Twisting - denoted by s (snub)
Each of these operations can be applied to the other regular figures based on 2D and 3D networks. Below we show how these operations work:

### Twisting

The squares revolve around 16.4675 ° and the triangles to -20.315 °.
24 levels have the triangles that arise after the rotation, forming a pentagonal icositetrahedron, which is built from the same pentagons.

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The pentagons revolve around 13.1064 ° and the triangles to -19.518 °. Similar results can be obtained in a pentagonal hexecontahedron after the operation s , where the Rhombeniksidodekaeder is transformed into the sloping dodecahedron (dodecahedron simum) is converted.

A polyhedron with tetrahedral symmetry, which all sides are irregular pentagons, is known under the name: Tetartoid or tetrahedral pentagonal dodecahedron .

o2c-1   o2c-2

## Other transformations

### Expansion

This may result in a polyhedron with tetrahedral symmetry.

Related to the 28-polyhedron are these two polyhedra:

The three polyhedra shown above can wrapped.

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