Elongated pentagonal pyramid

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Elongated pentagonal pyramid
Elongated pentagonal pyramid.png
Type Johnson
J8J9J10
Faces 5 triangles
5 squares
1 pentagon
Edges 20
Vertices 11
Vertex configuration 5(42.5)
5(32.42)
1(35)
Symmetry group C5v, [5], (*55)
Rotation group C5, [5]+, (55)
Dual polyhedron self-dual [1]
Properties convex
Net
Elongated Pentagonal Pyramid Net.svg
3D model of an elongated pentagonal pyramid J9 elongated pentagonal pyramid.stl
3D model of an elongated pentagonal pyramid

The elongated pentagonal pyramid is a polyhedron constructed by attaching one pentagonal pyramid onto one of the pentagonal prism's bases, a process known as elongation. It is an example of composite polyhedron. [2] [3] This construction involves the removal of one pentagonal face and replacing it with the pyramid. The resulting polyhedron has five equilateral triangles, five squares, and one pentagon as its faces. [4] It remains convex, with the faces are all regular polygons, so the elongated pentagonal pyramid is Johnson solid, enumerated as the sixteenth Johnson solid . [5]

For edge length , an elongated pentagonal pyramid has a surface area by summing the area of all faces, and volume by totaling the volume of a pentagonal pyramid's Johnson solid and regular pentagonal prism: [4]

The elongated pentagonal pyramid has a dihedral between its adjacent faces: [6]

References

  1. Draghicescu, Mircea. "Dual Models: One Shape to Make Them All". In Torrence, Eva; Torrence, Bruce; Séquin, Carlo H.; McKenna, Douglas; Fenyvesi, Kristóf; Sarhangi, Reza (eds.). Bridges Finland: Mathematics, Music, Art, Architecture, Education, Culture (PDF). pp. 635–640.
  2. Timofeenko, A. V. (2010). "Junction of Non-composite Polyhedra" (PDF). St. Petersburg Mathematical Journal. 21 (3): 483–512. doi:10.1090/S1061-0022-10-01105-2.
  3. Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. p. 8489. doi:10.1007/978-93-86279-06-4. ISBN   978-93-86279-06-4.
  4. 1 2 Berman, Martin (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR   0290245.
  5. Uehara, Ryuhei (2020). Introduction to Computational Origami: The World of New Computational Geometry. Springer. p. 62. doi:10.1007/978-981-15-4470-5. ISBN   978-981-15-4470-5. S2CID   220150682.
  6. Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics . 18: 169–200. doi: 10.4153/cjm-1966-021-8 . MR   0185507. S2CID   122006114. Zbl   0132.14603.