Images . Truncated icosahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments
Generating Elements of mesh modeling the surfaces of polyhedron, its dual image and the coloring of their edges and faces can be found in the applet.
![Image](https://beta.geogebra.org/resource/fcrej66p/3Ptx7JZSFOlUkfv2/material-fcrej66p.png)
Elements in polyhedron Biscribed Pentakis Dodecahedron(3) -Truncated icosahedron:
Vertices: V=60.
Faces: F =32. 12{5}+20{6}
Edges: E =90.
Truncated icosahedron:
https://en.wikipedia.org/wiki/Truncated_icosahedron
http://dmccooey.com/polyhedra/TruncatedIcosahedron.html
Vertices: 60 (60[3])
Faces: 32 (12 regular pentagons + 20 regular hexagons)
Edges: 90
![Image](https://beta.geogebra.org/resource/mcyyyjsz/AEvdCImsWYDyJCa3/material-mcyyyjsz.png)
![Image](https://beta.geogebra.org/resource/hpbzzau5/A4fO0B25wWOeppFM/material-hpbzzau5.png)
![Image](https://beta.geogebra.org/resource/zj2ufwz3/w4xs7Yj76lDUGOpx/material-zj2ufwz3.png)
The elements of the dual to the Biscribed Pentakis Dodecahedron(3)- Pentakis dodecahedron:
Vertices: V =32.
Faces: F =60. 60{3}
Edges: E =90. 60+30- The order of the number of edges in this polyhedron are according to their length.
Pentakis dodecahedron:
https://en.wikipedia.org/wiki/Pentakis_dodecahedron
http://dmccooey.com/polyhedra/PentakisDodecahedron.html
Vertices: 32 (12[5] + 20[6])
Faces: 60 (isosceles triangles)
Edges: 90 (60 short + 30 long)
![Image](https://beta.geogebra.org/resource/yp4wb8av/GfEzFiLi0KL64dis/material-yp4wb8av.png)