Triangular hebesphenorotunda (EntityTopic, 14)

From Hi.gher. Space

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The '''triangular hebesphenorotunda''' is the 92nd [[Johnson solid]], J92.
The '''triangular hebesphenorotunda''' is the 92nd [[Johnson solid]], J92.
<[#embed [hash DYC2MD9DJ7SPGS4AHA2DTT7S0C]]>
<[#embed [hash DYC2MD9DJ7SPGS4AHA2DTT7S0C]]>
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== Coordinates ==
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The following coordinates describe a triangular hebesphenorotunda with edge length 2, with its 3-fold axis of symmetry aligned to the Z axis:
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:The top triangle:
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::<0, 2/√3, 2*φ^2/√3>
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::<±1, -1/√3, 2*φ^2/√3>
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:The base of the triangles surrounding the top triangle:
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::<±1, φ^3/√3, 2*φ/√3>
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::<±φ^2, -1/(φ*√3), 2*φ/√3>
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::<±φ, -(φ+2)/√3, 2*φ/√3>
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:The tips of the pentagons:
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::<±φ^2, φ^2/√3, 2/√3>
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::<0, -2*φ^2/√3, 2/√3>
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:The hexagonal base
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::<±1, ±√3, 0>
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::<±2, 0, 0>
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where φ=(1+√5)/2 is the Golden Ratio.
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<[#polytope [id 77]]>
{{Trishapes}}
{{Trishapes}}

Latest revision as of 22:11, 2 March 2014

The triangular hebesphenorotunda is the 92nd Johnson solid, J92.

(image)

Coordinates

The following coordinates describe a triangular hebesphenorotunda with edge length 2, with its 3-fold axis of symmetry aligned to the Z axis:

The top triangle:
<0, 2/√3, 2*φ^2/√3>
<±1, -1/√3, 2*φ^2/√3>
The base of the triangles surrounding the top triangle:
<±1, φ^3/√3, 2*φ/√3>
<±φ^2, -1/(φ*√3), 2*φ/√3>
<±φ, -(φ+2)/√3, 2*φ/√3>
The tips of the pentagons:
<±φ^2, φ^2/√3, 2/√3>
<0, -2*φ^2/√3, 2/√3>
The hexagonal base
<±1, ±√3, 0>
<±2, 0, 0>

where φ=(1+√5)/2 is the Golden Ratio.

Incidence matrix

Dual: J92 dual

#TXIDVaVbVcVdEaEbEcEdEeEfEgEh3a5a3b4a3c3d6aTypeName
0 Va = point ; top
1 Vb = point ; mid
2 Vc = point ; cross
3 Vd = point ; bot
4 Ea 2000 = digon ; top to pen
5 Eb 1100 = digon ; pen to tola
6 Ec 0200 = digon ; tola to square
7 Ed 0110 = digon ; pen to bola
8 Ee 0101 = digon ; bola to square
9 Ef 0011 = digon ; bola to lat
10 Eg 0002 = digon ; square to bot
11 Eh 0002 = digon ; lat to bot
12 3a 300030000000 = triangle ; top
13 5a 221012020000 = pentagon ; pen
14 3b 120002100000 = triangle ; tola
15 4a 020200102010 = square ; square
16 3c 011100011100 = triangle ; bola
17 3d 001200000201 = triangle ; lat
18 6a 000600000033 = hexagon ; bot
19 C1a 3636363666331333631 = triangular hebesphenorotunda ;

Usage as facets


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
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