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)
“To be thoroughly conversant with a Man’s heart, is to take our final lesson in the iron-clasped volume of despair.”
—Edgar Allan Poe (1809–1845)
“Measured by any standard known to science—by horse-power, calories, volts, mass in any shape,—the tension and vibration and volume and so-called progression of society were full a thousand times greater in 1900 than in 1800;Mthe force had doubled ten times over, and the speed, when measured by electrical standards as in telegraphy, approached infinity, and had annihilated both space and time. No law of material movement applied to it.”
—Henry Brooks Adams (1838–1918)