# Dicone (EntityTopic, 11)

(Difference between revisions)
 Revision as of 20:43, 11 February 2014 (view source)Hayate (Talk | contribs)m (K6.4 upgrade: img -> embed)← Older edit Latest revision as of 18:19, 24 April 2018 (view source) Line 28: Line 28: *The [[realmic]] [[cross-section]]s (''n'') of a dicone are: *The [[realmic]] [[cross-section]]s (''n'') of a dicone are:
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+ + == Cross-sections == + Disk-first: + <[#embed [hash QVCBEZBV33HTT7ST4B6DJE0CC0]]> + Edge-first: + <[#embed [hash SCYDWNKQJFQ8GJGE4JFGW8EKQD]]> + Cone-first: + <[#embed [hash 7Z0WP548YGM1PMNAXA7YYXCSF5]]> == Projection == == Projection ==

## Latest revision as of 18:19, 24 April 2018

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.

## Equations

• 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
Unknown

## Cross-sections

Disk-first: Edge-first: Cone-first:

## Projection

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: pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron Powertopes: triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate Circular: glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder Torii: tiger • torisphere • spheritorus • torinder • ditorus