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Polyhedron (homeomorphic to a sphere) consisting of equilateral triangles only. If we define the valency of a sphere as the number of rods connected to it, and write the number of spheres with valencies 3, 4, 5, 6, ..., as n3,n4,n5,n6,... , this provides a rudimentary classification: (Note that there may be several shapes with the same signature)

(n3,n4,n5,n6,...)-deltahedron.

(go until the largest valency in your deltahedron)

This deltahedron then contains (n3+n4+n5+n6+...) spheres, and (3.n3+4.n4+5.n5+6.n6+...)/2 rods.

Also, using Euler's formula, it is easy to show that

3\,n_3+2\,n_4+n_5-n_7-2\,n_8-3\,n_9-4\,n_{10}-\cdots -(k-6)\,n_k-\cdots=12

Related Links Edit

Models Edit

(0,0,12,10)-deltahedron
(0 0 12 10) deltahedron
'
TypeDeltahedron
Rods 60 × Geomag rod icon
Spheres 22 × Geomag ball icon
Author Amafirlian 23:00, 1 July 2007 (UTC)


(0,0,12,16)-deltahedron
(0 0 12 16) deltahedron
'
TypeDeltahedron
Rods 78 × Geomag rod icon
Spheres 28 × Geomag ball icon
Author Amafirlian 10:44, 12 July 2007 (UTC)


(0,0,12,17)-deltahedron
(0 0 12 17) deltahedron
'
TypeDeltahedron
Rods 81 × Geomag rod icon
Spheres 29 × Geomag ball icon
Author Amafirlian 18:43, 1 July 2007 (UTC)


(0,0,12,20)-deltahedron
(0 0 12 20) deltahedron
'
TypeDeltahedron
Rods 90 × Geomag rod icon
Spheres 32 × Geomag ball icon
Author Amafirlian 18:45, 1 July 2007 (UTC)


(0,0,12,42)-deltahedron
(0 0 12 42) deltahedron
'
TypeDeltahedron
Rods 156 × Geomag rod icon
Spheres 54 × Geomag ball icon
Author Amafirlian 14:16, 21 July 2007 (UTC)


(0,0,12,45)-deltahedron
(0 0 12 45) deltahedron
'
TypeDeltahedron
Rods 165 × Geomag rod icon
Spheres 57 × Geomag ball icon
Author Amafirlian 13:30, 15 July 2007 (UTC)


(0,0,12,8)-deltahedron
(0 0 12 8) deltahedron
'
TypeDeltahedron
Rods 62 × Geomag rod icon
Spheres 20 × Geomag ball icon
Author Amafirlian 12:25, 12 July 2007 (UTC)


(0,0,18,32,6)-deltahedron
(0 0 18 32 6)-deltahedron
'
TypeDeltahedron
Rods 162 × Geomag rod icon
Spheres 56 × Geomag ball icon
Author Amafirlian 08:14, 22 July 2007 (UTC)


(0,12,0,36,6,3)-deltahedron
(0 12 0 36 6 3) deltahedron
'
TypeDeltahedron
Rods 165 × Geomag rod icon
Spheres 57 × Geomag ball icon
Author Amafirlian 23:41, 16 March 2008 (UTC)


(0,18,0,80,24)-deltahedron
(0 18 0 80 24)-deltahedron
'
TypeDeltahedron
Rods 360 × Geomag rod icon
Spheres 122 × Geomag ball icon
Author Amafirlian 15:42, 26 July 2007 (UTC)


(0,24,12,0,0,0,8,6)-deltahedron
(0 24 12 0 0 0 8 6)-deltahedron
Wedge-deltified rhombic dodecahedron
TypeDeltahedron
Rods 144 × Geomag rod icon
Spheres 50 × Geomag ball icon
Author Amafirlian 20:13, 2 August 2007 (UTC)


128-hedron
128-hedron
(0,6,60,0)-deltahedron
TypeDeltahedron
Rods 192 × Geomag rod icon
Spheres 66 × Geomag ball icon
Author Amafirlian 00:25, 10 June 2007 (UTC)


Creased Platonic Deltahedra
Cpp 5 2 2 s
'
TypePolyhedron
Rods 3F(3p2+3pf+3p2)/2 × Geomag rod icon
Spheres 2+Rods/3 × Geomag ball icon
Author --Leo Dorst 07:45, 30 August 2008 (UTC)


Diamond lattice cell
Diamond large b
'
TypeDeltahedron?
Rods (420Y+120G+96R+120B) × Geomag rod icon
Spheres 224 × Geomag ball icon
Author --Leo Dorst 17:24, 11 September 2008 (UTC)


Diamond lattice cell
Diamond lattice s
'
TypeDeltahedron?
Rods (144Y+96R+48B) × Geomag rod icon
Spheres (72+3) × Geomag ball icon
Author --Leo Dorst 06:27, 30 August 2008 (UTC)


Extended Elongated Hexagonal Antiprism
Ext elongated hexagonal antiprism
(0,0,12,32)-deltahedron
TypeDeltahedron
Rods 126 × Geomag rod icon
Spheres 44 × Geomag ball icon
Author Amafirlian 21:36, 21 June 2007 (UTC)
after input from Peter Jepsen


Lobel Frames


Pentagonal Deltahedron
Pentagonal deltahedron
(0,0,12,45)-deltahedron
TypeDeltahedron
Rods 160 × Geomag rod icon
Spheres 57 × Geomag ball icon
Author Amafirlian 22:22, 27 June 2007 (UTC)


Pentagonal Torus
Pentagonal torus
'
TypeDeltahedron
Rods 120 × Geomag rod icon
Spheres 40 × Geomag ball icon
Author Amafirlian 08:29, 15 August 2007 (UTC)


Snub Disphenoid
Snub disphenoid
Johnson solid J84
TypeJohnson Solid
Rods 18 × Geomag rod icon
Spheres 8 × Geomag ball icon
Author Amafirlian 18:04, 23 July 2007 (UTC)


(0,0,12,24)-deltahedron
(0 0 12 24) deltahedron
'
TypeDeltahedron
Rods 102 × Geomag rod icon
Spheres 36 × Geomag ball icon
Author Amafirlian 23:12, 1 July 2007 (UTC)


Snub Expanded (0,0,12,17)-deltahedron
Snub exp (0 0 12 17) deltahedron
(0,0,12,38)-deltahedron
Type
Rods 144 × Geomag rod icon
Spheres 50 × Geomag ball icon
Author Amafirlian 13:16, 10 July 2007 (UTC)


Snub Expanded Snub Disphenoid
Snub exp snub disphenoid
(0,4,4,36)-deltahedron
TypeDeltahedron
Rods 126 × Geomag rod icon
Spheres 44 × Geomag ball icon
Author Amafirlian 19:55, 23 July 2007 (UTC)


Spiral Deltahedron
Spiral deltahedron
(0,0,12,30)-deltahedron
TypeDeltahedron
Panels 23 × Geomag triangle panel icon
Rods 120 × Geomag rod icon
Spheres 42 × Geomag ball icon
Author Amafirlian 08:44, 23 June 2007 (UTC)


Spiral sphere
Spiral sphere s
'
TypePolyhedron
Rods 123+63 × Geomag rod icon
Spheres 64 × Geomag ball icon
Author --Leo Dorst 15:10, 14 June 2008 (UTC)L.Dorst


3m-fold Torus
Torus6
'
TypePolyhedron:Torus
Rods 180 × Geomag rod icon
Spheres 108 × Geomag ball icon
Author Leo Dorst 06:58, 24 May 2008 (UTC)


5m-fold Torus
TenTorus
'
TypePolyhedron:Torus
Rods 300 × Geomag rod icon
Spheres 180 × Geomag ball icon
Author Leo Dorst 06:58, 24 May 2008 (UTC)


Small Torus
Tiny torus a
'
TypePolyhedron:Torus
Rods 108 × Geomag rod icon
Spheres 36 × Geomag ball icon
Author Leo Dorst 05:59, 6 September 2008 (UTC)


Squared Torus
Square torus a
'
TypePolyhedron:Torus
Rods 198 × Geomag rod icon
Spheres 66 × Geomag ball icon
Author --Leo Dorst 19:26, 20 September 2008 (UTC)


Tiny Torus
Teensy torus a
'
TypePolyhedron:Torus
Rods 72 × Geomag rod icon
Spheres 24 × Geomag ball icon
Author ----Leo Dorst 19:26, 21 September 2008 (UTC)


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