Function Repository Resource:

# Tetartoid

Get a tetartoid given three values

Contributed by: Ed Pegg Jr (Wolfram Research)
 ResourceFunction["Tetartoid"][{a,b,c}] returns a tetartoid, given the non-negative values a,b and c. ResourceFunction["Tetartoid"][{a,b,c},"Polyhedron"] returns a tetartoid represented as a Polyhedron object.

## Details

A tetartoid is a dodecahedron with 12 identical irregular pentagonal faces and that has chiral tetrahedral symmetry (point group T in Schönflies notation).
In cases of degeneracy, a default tetartoid will be returned instead.

## Examples

### Basic Examples (1)

A sample tetartoid:

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### Scope (4)

Return a tetartoid as a Polyhedron object:

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 In[3]:=
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Compute its surface area and volume:

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The tetartoid generally has chiral tetrahedral symmetry:

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The tetartoid can have dodecahedral symmetry:

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The tetartoid can have cubic symmetry:

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### Possible Issues (1)

The construction calculates some denominators that cannot be zero. In cases where a zero is encountered, a default tetartoid is substituted:

 Out[7]=

## Requirements

Wolfram Language 11.3 (March 2018) or above

## Version History

• 1.1.0 – 07 July 2021
• 1.0.0 – 15 February 2019