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:
“Although volume upon volume is written to prove slavery a very good thing, we never hear of the man who wishes to take the good of it, by being a slave himself.”
—Abraham Lincoln (1809–1865)
“A big leather-bound volume makes an ideal razorstrap. A thin book is useful to stick under a table with a broken caster to steady it. A large, flat atlas can be used to cover a window with a broken pane. And a thick, old-fashioned heavy book with a clasp is the finest thing in the world to throw at a noisy cat.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“A tattered copy of Johnson’s large Dictionary was a great delight to me, on account of the specimens of English versifications which I found in the Introduction. I learned them as if they were so many poems. I used to keep this old volume close to my pillow; and I amused myself when I awoke in the morning by reciting its jingling contrasts of iambic and trochaic and dactylic metre, and thinking what a charming occupation it must be to “make up” verses.”
—Lucy Larcom (1824–1893)