FANDOM


One thing I've just read about today are complex polytopes. Polytopes are some collection of points, lines, faces and so in in the space \mathbb{R}^X (that is, the coordinates of all points are real). However, in the space \mathbb{C}^X, you get a whole bunch of new polytopes! As a plus side, you can recover your original real polytopes by constraining your imaginary parts to 0.

Polycomtela

Just as a polytelon is two connected points on the real line, a complex polytelon is a group of connected points on a complex line. Represented on an argand plane, these will look like polygons (and become polygons, if you split the complex number into real and imaginary parts), but make no mistake: every point on a complex polytelon can be represented by a single complex number.

Name Schlafli Symbol Vertices Notes
Dicomtelon _2 \{ \} 2 points Real line segment
P-comtelon _p \{ \} p points

Polycomgons

A polycomgon is made up of multiple connected polycomtela. The naming scheme used identifies each one with an element, which is based off the Shephard-Todd number of its complex symmetry group.

Name Schlafli Symbol Vertices Edges Notes
P-gon _2 \{ p \} _2 p points p line segments Real P-gon
P-comtelal duoprism _p \{ 4 \} _2 p2 points 2p P-comtela
P-comtelal duopyramid _2 \{ 4 \} _p 2p points p2 line segments
Berylocomgon _3 \{ 3 \} _3 8 points 8 tricomtela The Möbius–Kantor configuration
Carbocomgon _3 \{6\} _2 24 points 16 tricomtela
Dual carbocomgon _2 \{6\} _3 16 points 24 line segments
Borocomgon _3 \{4\} _3 24 points 24 tricomtela
Oxycomgon _4 \{3\} _4 24 points 24 tetracomtela
Silicocomgon _3 \{8\} _2 72 points 48 tricomtela
Dual silicocomgon _2 \{8\} _3 48 points 72 line segments
Fluorocomgon _4 \{6\} _2 96 points 48 tricomtela
Dual fluorocomgon _2 \{6\} _4 48 points 96 line segments
Neocomgon _4 \{4\} _3 96 points 72 tetracomtela
Dual neocomgon _3 \{4\} _4 72 points 96 tricomtela
Calcocomgon _3 \{5\} _3 120 points 120 tricomtela
Sulphocomgon _5 \{3\} _5 120 points 120 pentacomtela
Scandocomgon _3 \{10\} _2 360 points 240 tricomtela
Dual scandocomgon _2 \{10\} _3 240 points 360 line segments
Chlorocomgon _5 \{6\} _2 600 points 240 pentacomtela
Dual chlorocomgon _2 \{6\} _5 240 points 600 line segments
Argocomgon _5 \{4\} _3 600 points 360 pentacomtela
Dual argocomgon _3 \{4\} _5 360 points 600 tricomtela

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.