Volume
The volume of J35 can be calculated as follows:
J35 consists of 2 cupolae and hexagonal prism.
The two cupolae makes 1 cuboctahedron = 8 tetrahedra + 6 half-octahedra. 1 octahedron = 4 tetrahedra, so total we have 20 tetrahedra.
What is the volume of a tetrahedron? Construct a tetrahedron having vertices in common with alternate vertices of a cube (of side, if tetrahedron has unit edges). The 4 triangular pyramids left if the tetrahedron is removed from the cube form half an octahedron = 2 tetrahedra. So
The hexagonal prism is more straightforward. The hexagon has area, so
Finally
numerical value:
Read more about this topic: Elongated Triangular Orthobicupola
Famous quotes containing the word volume:
“Thy commandment all alone shall live
Within the book and volume of my brain
Unmixed with baser matter.”
—William Shakespeare (1564–1616)
“F.R. Leavis’s “eat up your broccoli” approach to fiction emphasises this junkfood/wholefood dichotomy. If reading a novel—for the eighteenth century reader, the most frivolous of diversions—did not, by the middle of the twentieth century, make you a better person in some way, then you might as well flush the offending volume down the toilet, which was by far the best place for the undigested excreta of dubious nourishment.”
—Angela Carter (1940–1992)
“There is a note in the front of the volume saying that no public reading ... may be given without first getting the author’s permission. It ought to be made much more difficult to do than that.”
—Robert Benchley (1889–1945)