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Function Repository Resource:

Tetartoid

Source Notebook

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:

In[1]:=
ResourceFunction["Tetartoid"][{1, 2, 3}]
Out[1]=

Scope (4) 

Return a tetartoid as a Polyhedron object:

In[2]:=
ResourceFunction["Tetartoid"][{1, 2, 3}, "Polyhedron"]
Out[2]=
In[3]:=
InputForm[%]
Out[3]=

Compute its surface area and volume:

In[4]:=
{SurfaceArea[%], Volume[%]}
Out[4]=

The tetartoid generally has chiral tetrahedral symmetry:

In[5]:=
ResourceFunction["Tetartoid"][{20, 21, 22}]
Out[5]=

The tetartoid can have dodecahedral symmetry:

In[6]:=
ResourceFunction["Tetartoid"][{0, 2, 5}]
Out[6]=

The tetartoid can have cubic symmetry:

In[7]:=
ResourceFunction["Tetartoid"][{5, 6, 6}]
Out[7]=

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

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