Sphenocorona (EntityTopic, 14)

(Difference between revisions)
 Revision as of 01:24, 2 February 2018 (view source)Quickfur (Talk | contribs) (Add sphenocorona with coordinates)← Older edit Latest revision as of 01:20, 10 February 2018 (view source)Quickfur (Talk | contribs) m (→Cartesian coordinates: +sp) Line 34: Line 34: :C = 1.914399800381786 :C = 1.914399800381786 :D = 1.578855253321743 :D = 1.578855253321743 - :E =2.626590848527109 + :E = 2.626590848527109 == Images == == Images ==

Latest revision as of 01:20, 10 February 2018

The sphenocorona is the 86th Johnson solid, J86.

Cartesian coordinates

The Cartesian coordinates of the sphenocorona, resting on the origin and with edge length 2, are:

(0, 0, ±1)
(±A, B, ±1)
(0, C, ±D)
(±1, E, 0)

where A, B, C, D, E are roots of the following polynomials:

 92 + 112A - 100A² - 24A³ + 15A⁴ 1 < A < 2 3600 - 96B² - 3176B⁴ - 24B⁶ + 225B⁸ 1 < B < 1.5 3600 - 96C² - 3176C⁴ - 24C⁶ + 225C⁸ 1.5 < C < 2 95 + 100D - 82D² - 36D³ + 15D⁴ 1 < D < 2 -20 - 4E² + E⁴ 1 < E < 2

Or, in closed form:

A = (1/15)(6 + √6 + 2√(213 - 57√6))
B = (2/5)√(1/6 + 6√6 - (1/3)√(538 + 18√6))
C = (2/5)√(1/6 + 6√6 + (1/3)√(538 + 18√6))
D = (1/15)(9 - √6 + 2√(213 - 57√6))
E = √(2(1 + √6))

Their numerical values are approximately:

A = 1.705453885692834
B = 1.044713857367277
C = 1.914399800381786
D = 1.578855253321743
E = 2.626590848527109

Images

 Notable Trishapes Regular: tetrahedron • cube • octahedron • dodecahedron • icosahedron Direct truncates: tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate Mesotruncates: stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron Snubs: snub staurohedron • snub rhodohedron Curved: sphere • torus • cylinder • cone • frustum • crind