elongated pentagonal gyrobirotunda

{{Infobox polyhedron

|image=elongated_pentagonal_gyrobirotunda.png

|type=Johnson
{{math|elongated pentagonal orthobirotunda – J{{sub|43}} – gyroelongated triangular bicupola}}

|faces=10+10 triangles
10 squares
2+10 pentagons

|edges=80

|vertices=40

|symmetry={{math|D{{sub|5d}}}}

|vertex_config={{math|20(3.4{{sup|2}}.5)
2.10(3.5.3.5)}}

|dual=-

|properties=convex

|net=Johnson solid 43 net.png

}}

In geometry, the elongated pentagonal gyrobirotunda or elongated icosidodecahedron is one of the Johnson solids ({{math|J{{sub|43}}}}). As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron (one of the Archimedean solids), by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae ({{math|J{{sub|6}}}}) through 36 degrees before inserting the prism yields an elongated pentagonal orthobirotunda ({{math|J{{sub|42}}}}).

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:Stephen Wolfram, "[http://www.wolframalpha.com/input/?i=Elongated+pentagonal+gyrobirotunda Elongated pentagonal gyrobirotunda]" from Wolfram Alpha. Retrieved July 26, 2010.

: $V=\frac{1}{6}\left(45+17\sqrt{5}+15\sqrt{5+2\sqrt{5}}\right)a^3 \approx 21.5297 a^3$

: $A=\left(10+\sqrt{30\left(10+3\sqrt{5}+\sqrt{75+30\sqrt{5}}\right)}\right)a^2 \approx 39.306 a^2$

References

External links

{{Mathworld2 | urlname = ElongatedPentagonalGyrobirotunda | title =Elongated pentagonal gyrobirotunda | urlname2 = JohnsonSolid | title2 = Johnson solid }}

Category:Johnson solids