Dicone (EntityTopic, 11)

From Hi.gher. Space

A dicone is a special case of a pyramid where the base is a cone. It is also a special case of a dipyramid where the base is a circle. It is bounded by two cones and an arrinder. Its faces are a circle and two curved-cone-surfaces.


  • Variables:
r ⇒ radius of base of dicone
h ⇒ height of dicone
  • The hypervolumes of a dicone are given by: (the red equations are thought to be inaccurate and need revising!)
total edge length = 2πr + h
total surface area = πr(r + 2√(r2 + h2))
surcell volume = πrh3 · (2r + √(r2 + h2))

bulk = π12 · r2h2


Disk-first: (image) Edge-first: (image) Cone-first: (image)


The following are the two possible types of parallel projections for a dicone:


The nappe-first parallel projection of the dicone into 3-space is a tetrahedron.

Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus

21. 1111
Triangular diprism
22. 22
23. [11]2
Square dipyramid
List of tapertopes