This page is under construction in the sense that the 3D models still need to be fine tuned.
This page presents interactive 3D models of the stellations of the rhombic triacontahedron. The 3D models have predefined camera points from which the different kind of symmetry axes are recognised. In the article The Stellations of the Rhombic Triacontahedron and beyond P. Messer presents a way to derive all fully supported stellations of the rhombic triacontahedron according to a set of rules. All models on this page are based on that set of rules and the presented methods were used to generate all models.
To be able to view and investigate the 3D models you need a X3D player. See note1. (Click here if you want to watch the models with a VRML player instead.)
The following table contains the list of fully supported reflexible stellations.
Name | Regions | X3D model | Name | Regions | X3D model | Name | Regions | X3D model |
A | 1a | Model | B | 2ab | Model | C | 2a, 3ac | Model |
CD | 3abc | Model | D | 2b, 3b | Model | DE | 3ab, 4ad | Model |
DG | 3ab, 4a, 5a | Model | E | 2a, 3a, 4ad | Model | EF | 4abcd | Model |
EI | 4acd, 5c | Model | F | 3c, 4bc | Model | FG | 4abc, 5a | Model |
G | 2a, 3a, 4a, 5a | Model | GH | 4b, 5abd | Model | GHI | 5abcd | Model |
GI | 4ac, 5ac | Model | GK | 5ad, 6bcd | Model | GM | 5ad, 6bd, 7be | Model |
GMN | 5ad, 6d, 7bcef | Model | GN | 5ad, 6cd, 7cf | Model | GQ | 5ad, 6d, 7ef, 8cf | Model |
GU | 5ad, 6d, 7ef, 8f, 9g | Model | H | 4bd, 5bd | Model | HI | 4d, 5bcd | Model |
I | 3c, 4c, 5c | Model | IJ | 5bc, 6a | Model | J | 4b, 5b, 6a | Model |
JK | 6abcd | Model | JM | 6abd, 7be | Model | JMN | 6ad, 7bcef | Model |
JN | 6acd, 7cf | Model | JQ | 6ad, 7ef, 8cf | Model | JU | 6ad, 7ef, 8f, 9g | Model |
K | 4d, 5d, 6bcd | Model | L | 6bc, 7ad | Model | LM | 6b, 7abde | Model |
LMN | 7abcdef | Model | LN | 6c, 7acdf | Model | LQ | 7adef, 8cf | Model |
LU | 7adef, 8f, 9g | Model | M | 4d, 5d, 6bd, 7be | Model | MN | 4d, 5d, 6d, 7bcef | Model |
MO | 7bcde, 8ad | Model | MR | 7bcde, 8d, 9ae | Model | N | 4d, 5d, 6cd, 7cf | Model |
NP | 7abcf, 8be | Model | NT | 7abcf, 8b, 9c | Model | O | 6c, 7cd, 8ad | Model |
OP | 7bc, 8abde | Model | OPQ | 8abcdef | Model | OPU | 8abdef, 9g | Model |
OQ | 7de, 8acdf | Model | OQT | 8abcdf, 9c | Model | OT | 7bc, 8abd, 9c | Model |
OTU | 8abdf, 9cg | Model | OU | 7de, 8adf, 9g | Model | P | 6b, 7ab, 8be | Model |
PQ | 7af, 8bcef | Model | PQR | 8bcdef, 9ae | Model | PR | 7bc, 8bde, 9ae | Model |
PRU | 8bdef, 9aeg | Model | PU | 7af, 8bef, 9g | Model | Q | 4d, 5d, 6d, 7ef, 8cf | Model |
QR | 7de, 8cdf, 9ae | Model | QRT | 8bcdf, 9ace | Model | QT | 7af, 8bcf, 9c | Model |
R | 6c, 7cd, 8d, 9ae | Model | RS | 8ce, 9abdef | Model | RST | 8c, 9abcdef | Model |
RSTU | 9abcdefg | Model | RSU | 8e, 9abdefg | Model | RT | 7bc, 8bd, 9ace | Model |
RTU | 8bdf, 9aceg | Model | RTW | 10bg, 9abcef | Model | RU | 7de, 8df, 9aeg | Model |
RUX | 10cd, 9abdeg | Model | RW | 10bg, 8e, 9abef | Model | RWX | 10bcdg, 9abe | Model |
RX | 10cd, 8c, 9abde | Model | R2A | 10bc, 11cf, 9abe | Model | S | 8ace, 9bdf | Model |
ST | 8ac, 9bcdf | Model | STU | 8a, 9bcdfg | Model | SU | 8ae, 9bdfg | Model |
T | 6b, 7ab, 8b, 9c | Model | TU | 7af, 8bf, 9cg | Model | TUV | 10aef, 9acdfg | Model |
TV | 10aef, 8c, 9acdf | Model | TVW | 10abefg, 9acf | Model | TW | 10bg, 8a, 9bcf | Model |
TZ | 10afg, 11be, 9acf | Model | U | 4d, 5d, 6d, 7ef, 8f, 9g | Model | UV | 10aef, 8e, 9adfg | Model |
UVX | 10acdef, 9adg | Model | UX | 10cd, 8a, 9bdg | Model | UY | 10ade, 11ad, 9adg | Model |
V | 10aef, 8ce, 9adf | Model | VW | 10abefg, 8e, 9af | Model | VWX | 10abcdefg, 9a | Model |
VX | 10acdef, 8c, 9ad | Model | V2A | 10abcef, 11cf, 9a | Model | W | 10bg, 8ae, 9bf | Model |
WX | 10bcdg, 8a, 9b | Model | WY | 10abdeg, 11ad, 9a | Model | X | 10cd, 8ac, 9bd | Model |
XZ | 10acdfg, 11be, 9a | Model | Y | 10ade, 11ad, 8c, 9ad | Model | YZ | 10adg, 11abde, 9a | Model |
YZ2A | 10a, 11abcdef, 9a | Model | Y2A | 10abe, 11acdf, 9a | Model | Z | 10afg, 11be, 8e, 9af | Model |
Z2A | 10acf, 11bcef, 9a | Model | 2A | 10bc, 11cf, 8a, 9b | Model | 2B | 10a, 11abf, 12abc, 9a | Model |
The following table contains the list of fully supported enantiomorphous stellations.
Name | Regions | X3D model | Name | Regions | X3D model |
E, (F)r | (4ad), (4bc)r, (3ab)l | Model | (F)r | (3c), (4bc)r, (3ab)l | Model |
G, (F)r | (4a, 5a), (4bc)r, (3ab)l | Model | G, (K)r | (5ad), (6bcd)r, (5bc)l | Model |
G, (Q)r | (5ad, 6d, 7ef), (8cf)r, (7bc)l | Model | J, (K)r | (6a), (6bcd)r, (5bc)l | Model |
J, (Q)r | (6ad, 7ef), (8cf)r, (7bc)l | Model | (K)r | (4d, 5d), (6bcd)r, (5bc)l | Model |
L, (Q)r | (7adef), (8cf)r, (7bc)l | Model | N, (P)r | (7abcf), (8be)r, (7de)l | Model |
O, (P)r | (7bc, 8ad), (8be)r, (7de)l | Model | OP, (Q)r | (8abde), (8cf)r, (7bc)l | Model |
OQ, (P)r | (8acdf), (8be)r, (7de)l | Model | O, (PQ)r | (8ad), (8bcef)r, (7bcde)l | Model |
O, (Q)l, (P)r | (8ad), (7bc, 8be)r, (7de, 8cf)l | Model | OU, (P)r | (8adf, 9g), (8be)r, (7de)l | Model |
O, (Q)r | (7de, 8ad), (8cf)r, (7bc)l | Model | OT, (Q)r | (8abd, 9c), (8cf)r, (7bc)l | Model |
(P)r | (6b, 7ab), (8be)r, (7de)l | Model | P, (Q)r | (7af, 8be), (8cf)r, (7bc)l | Model |
Q, (P)r | (7af, 8cf), (8be)r, (7de)l | Model | (PQ)r | (7af), (8bcef)r, (7bcde)l | Model |
(Q)l, (P)r | (7af), (7bc, 8be)r, (7de, 8cf)l | Model | PR, (Q)r | (8bde, 9ae), (8cf)r, (7bc)l | Model |
QR, (P)r | (8cdf, 9ae), (8be)r, (7de)l | Model | R, (PQ)r | (8d, 9ae), (8bcef)r, (7bcde)l | Model |
R, (Q)l, (P)r | (8d, 9ae), (7bc, 8be)r, (7de, 8cf)l | Model | R, (P)r | (7bc, 8d, 9ae), (8be)r, (7de)l | Model |
RU, (P)r | (8df, 9aeg), (8be)r, (7de)l | Model | U, (P)r | (7af, 8f, 9g), (8be)r, (7de)l | Model |
(Q)r | (4d, 5d, 6d, 7ef), (8cf)r, (7bc)l | Model | R, (Q)r | (7de, 8d, 9ae), (8cf)r, (7bc)l | Model |
RT, (Q)r | (8bd, 9ace), (8cf)r, (7bc)l | Model | T, (Q)r | (7af, 8b, 9c), (8cf)r, (7bc)l | Model |
R, (S)r | (8ce, 9ae), (9bdf)r, (8bdf)l | Model | R, (PS)r | (8c, 9ae), (8e, 9bdf)r, (7de, 8df)l | Model |
R, (QS)r | (8e, 9ae), (8c, 9bdf)r, (7bc, 8bd)l | Model | R, (PQS)r | (9ae), (8ce, 9bdf)r, (7bcde, 8d)l | Model |
RT, (S)r | (8c, 9ace), (9bdf)r, (8bdf)l | Model | RT, (QS)r | (9ace), (8c, 9bdf)r, (7bc, 8bd)l | Model |
RTU, (S)r | (9aceg), (9bdf)r, (8bdf)l | Model | RU, (S)r | (8e, 9aeg), (9bdf)r, (8bdf)l | Model |
RU, (PS)r | (9aeg), (8e, 9bdf)r, (7de, 8df)l | Model | RU, (X)r | (9abdeg), (10cd)r, (9cf)l | Model |
RU, (SX)r | (9aeg), (10cd, 9bd)r, (8bdf, 9c)l | Model | RW, (X)r | (10bg, 9abe), (10cd)r, (9cf)l | Model |
R, (X)r | (8c, 9abde), (10cd)r, (9cf)l | Model | R, (SX)r | (8c, 9ae), (10cd, 9bd)r, (8bdf, 9c)l | Model |
R, (QSX)r | (9ae), (10cd, 8c, 9bd)r, (7bc, 8bd, 9c)l | Model | (S)r | (8ace), (9bdf)r, (8bdf)l | Model |
(PS)r | (8ac), (8e, 9bdf)r, (7de, 8df)l | Model | (QS)r | (8ae), (8c, 9bdf)r, (7bc, 8bd)l | Model |
(PQS)r | (8a), (8ce, 9bdf)r, (7bcde, 8d)l | Model | T, (S)r | (8ac, 9c), (9bdf)r, (8bdf)l | Model |
T, (QS)r | (8a, 9c), (8c, 9bdf)r, (7bc, 8bd)l | Model | TU, (S)r | (8a, 9cg), (9bdf)r, (8bdf)l | Model |
U, (S)r | (8ae, 9g), (9bdf)r, (8bdf)l | Model | U, (PS)r | (8a, 9g), (8e, 9bdf)r, (7de, 8df)l | Model |
TU, (V)r | (9acdfg), (10aef)r, (9be)l | Model | TU, (SV)r | (9acg), (10aef, 9df)r, (8bdf, 9e)l | Model |
T, (V)r | (8c, 9acdf), (10aef)r, (9be)l | Model | T, (SV)r | (8c, 9ac), (10aef, 9df)r, (8bdf, 9e)l | Model |
T, (QSV)r | (9ac), (10aef, 8c, 9df)r, (7bc, 8bd, 9e)l | Model | TW, (V)r | (10bg, 9acf), (10aef)r, (9be)l | Model |
T, (Z)r | (10afg, 9acf), (11be)r, (10be)l | Model | T, (VZ)r | (10g, 9acf), (10af, 11be)r, (10b, 9be)l | Model |
U, (V)r | (8e, 9adfg), (10aef)r, (9be)l | Model | U, (SV)r | (8e, 9ag), (10aef, 9df)r, (8bdf, 9e)l | Model |
U, (PSV)r | (9ag), (10aef, 8e, 9df)r, (7de, 8df, 9e)l | Model | UV, (X)r | (10aef, 9adg), (10cd)r, (9cf)l | Model |
UX, (V)r | (10cd, 9adg), (10aef)r, (9be)l | Model | U, (VX)r | (9adg), (10acdef)r, (9bcef)l | Model |
U, (X)l, (V)r | (9adg), (10aef, 9cf)r, (10cd, 9be)l | Model | U, (SVX)r | (9ag), (10acdef, 9d)r, (8bdf, 9ce)l | Model |
U, (X)r | (8a, 9bdg), (10cd)r, (9cf)l | Model | U, (SX)r | (8a, 9g), (10cd, 9bd)r, (8bdf, 9c)l | Model |
(V)r | (8ce, 9adf), (10aef)r, (9be)l | Model | (SV)r | (8ce, 9a), (10aef, 9df)r, (8bdf, 9e)l | Model |
(PSV)r | (8c, 9a), (10aef, 8e, 9df)r, (7de, 8df, 9e)l | Model | (QSV)r | (8e, 9a), (10aef, 8c, 9df)r, (7bc, 8bd, 9e)l | Model |
(PQSV)r | (9a), (10aef, 8ce, 9df)r, (7bcde, 8d, 9e)l | Model | W, (V)r | (10bg, 8e, 9af), (10aef)r, (9be)l | Model |
VW, (X)r | (10abefg, 9a), (10cd)r, (9cf)l | Model | WX, (V)r | (10bcdg, 9a), (10aef)r, (9be)l | Model |
W, (VX)r | (10bg, 9a), (10acdef)r, (9bcef)l | Model | W, (X)l, (V)r | (10bg, 9a), (10aef, 9cf)r, (10cd, 9be)l | Model |
V, (X)r | (10aef, 8c, 9ad), (10cd)r, (9cf)l | Model | X, (V)r | (10cd, 8c, 9ad), (10aef)r, (9be)l | Model |
(VX)r | (8c, 9ad), (10acdef)r, (9bcef)l | Model | (X)l, (V)r | (8c, 9ad), (10aef, 9cf)r, (10cd, 9be)l | Model |
(SVX)r | (8c, 9a), (10acdef, 9d)r, (8bdf, 9ce)l | Model | (QSVX)r | (9a), (10acdef, 8c, 9d)r, (7bc, 8bd, 9ce)l | Model |
2A, (V)r | (10bc, 11cf, 9a), (10aef)r, (9be)l | Model | W, (X)r | (10bg, 8a, 9b), (10cd)r, (9cf)l | Model |
(X)r | (8ac, 9bd), (10cd)r, (9cf)l | Model | (SX)r | (8ac), (10cd, 9bd)r, (8bdf, 9c)l | Model |
(QSX)r | (8a), (10cd, 8c, 9bd)r, (7bc, 8bd, 9c)l | Model | X, (Z)r | (10acdfg, 9a), (11be)r, (10be)l | Model |
Z, (X)r | (10afg, 11be, 9a), (10cd)r, (9cf)l | Model | (XZ)r | (10afg, 9a), (10cd, 11be)r, (10be, 9cf)l | Model |
(Z)l, (X)r | (10afg, 9a), (10bcde)r, (11be, 9cf)l | Model | X, (VZ)r | (10cdg, 9a), (10af, 11be)r, (10b, 9be)l | Model |
(VXZ)r | (10g, 9a), (10acdf, 11be)r, (10b, 9bcef)l | Model | (VZ)l, (X)r | (10g, 9a), (10bcd, 9be)r, (10af, 11be, 9cf)l | Model |
Y, (Z)r | (10adg, 11ad, 9a), (11be)r, (10be)l | Model | Y2A, (Z)r | (10a, 11acdf, 9a), (11be)r, (10be)l | Model |
(Z)r | (10afg, 8e, 9af), (11be)r, (10be)l | Model | (VZ)r | (10g, 8e, 9af), (10af, 11be)r, (10b, 9be)l | Model |
2A, (Z)r | (10acf, 11cf, 9a), (11be)r, (10be)l | Model | 2A, (VZ)r | (10c, 11cf, 9a), (10af, 11be)r, (10b, 9be)l | Model |
(2B)r | (10a, 11abf, 9a), (12abc)r, (11cde)l | Model | (Z2B)r | (10a, 11af, 9a), (11b, 12abc)r, (10be, 11cd)l | Model |
2006-02-18, 23:24