srid

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Acronym srid

TOCID symbol rID

Name small rhombicosidodecahedron,
expanded icosahedron,
expanded dodecahedron

©

VRML

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Circumradius sqrt[sqrt(5)+11/4] = 2.232951

Vertex figure [3,4,5,4] = xf&#q

Vertex layers

Layer	Symmetry	Subsymmetries
	`o3o5o`	`o3o .`	`o . o`	`. o5o`
1	`x3o5x`	`x3o .` {3} first	`x . x` {4} first	`. o5x` {5} first
2		`x3f .`	`o . F`	`. x5x`
3a		`o3V .`	`F . f`	`. x5f`
3b		`F3x .`	`F . f`	`. x5f`
4a		`f3F .`	`A . o`	`. F5o`
4b		`f3F .`	`f . V`	`. F5o`
5		`V3x .`	`V . F`	`. o5F`
6a		`x3V .`	`x . B`	`. f5x`
6b		`x3V .`	`B . x`	`. f5x`
7		`F3f .`	`F . A`	`. x5x`
8a		`V3o .`	`x . B`	`. x5o` opposite {5}
8b		`x3F .`	`B . x`	`. x5o` opposite {5}
9		`f3x .`	`V . F`
10a		`o3x .` opposite {3}	`A . o`
10b		`o3x .` opposite {3}	`f . V`
11			`F . f`
12			`o . F`
13			`x . x` opposite {4}

(F=ff=f+x, V=2f, A=F+x=f+u=f+2x, B=V+x=2f+x)

Coordinates

(τ³/2, 1/2, 1/2) & all permutations, all changes of sign
(τ, τ²/2, τ/2) & even permutations, all changes of sign
(τ²/2, 1+τ/2, 0) & even permutations, all changes of sign

where τ = (1+sqrt(5))/2

General of army (is itself convex)

Colonel of regiment (is itself locally convex – other uniform polyhedral members: saddid sird – other edge facetings)

Dihedral angles

between {3} and {4}: arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
between {4} and {5}: arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°

Dual sladit

Face vector 60, 120, 62

Confer

Grünbaumian relatives:: 2srid
related Johnson solids:: pecu dirid gyrid pabidrid mabidrid pagydrid magydrid gybadrid bagydrid tagyrid tedrid
facetings:: noble {9,3} modwrap
variations:: a3b5c q3o5x f3o5x x3o5f v3o5f
ambification:: resrid
general polytopal classes:: Wythoffian polyhedra

External
links

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As abstract polytope srid is isomorphic to qrid, thereby replacing prograde pentagons by retrograde pentagrams.

The right image shows where the rhombi part of its name comes from: in fact it also can be seen as a rectified version of the rhombi-triacontahedron.

When looking more into classes of isogonal variants, then this polyhedron also could be addressed as a rectified icosidodecahedron. However true rectification would not produce squares there. In fact it rather would produce x3o5f instead.

Note that srid can be thought of as the external blend of 1 cube + 8 peppies + 12 bilbiros + 6 G3s, cf. the right Steward toroid E5 \ 6J91(P4).

Incidence matrix according to Dynkin symbol

x3o5x

. . . | 60 |  2  2 |  1  2  1
------+----+-------+---------
x . . |  2 | 60  * |  1  1  0
. . x |  2 |  * 60 |  0  1  1
------+----+-------+---------
x3o . |  3 |  3  0 | 20  *  *
x . x |  4 |  2  2 |  * 30  *
. o5x |  5 |  0  5 |  *  * 12

snubbed forms: β3o5x, x3o5β, β3o5β

x5/4o3/2x 

.   .   . | 60 |  2  2 |  1  2  1
----------+----+-------+---------
x   .   . |  2 | 60  * |  1  1  0
.   .   x |  2 |  * 60 |  0  1  1
----------+----+-------+---------
x5/4o   . |  5 |  5  0 | 12  *  *
x   .   x |  4 |  2  2 |  * 30  *
.   o3/2x |  3 |  0  3 |  *  * 20

oxxFofxx5xxfoFxxo&#xt   → height(1,2) = height(3,4) = height(5,6) = height(7,8) = sqrt[(5-sqrt(5))/10] = 0.525731
                          height(2,3) = height(6,7) = sqrt[(5+sqrt(5))/10] = 0.850651
                          height(4,5) = sqrt[(5-2 sqrt(5))/5] = 0.324920

o.......5o.......     | 5  *  * * *  *  * * | 2  2 0 0  0 0  0  0  0  0 0  0 0 0  0 0 | 1 1 2 0 0 0  0 0 0 0 0 0 0
.o......5.o......     | * 10  * * *  *  * * | 0  1 1 1  1 0  0  0  0  0 0  0 0 0  0 0 | 0 1 1 1 1 0  0 0 0 0 0 0 0
..o.....5..o.....     | *  * 10 * *  *  * * | 0  0 0 0  1 1  1  1  0  0 0  0 0 0  0 0 | 0 0 0 1 1 1  1 0 0 0 0 0 0
...o....5...o....     | *  *  * 5 *  *  * * | 0  0 0 0  0 0  2  0  2  0 0  0 0 0  0 0 | 0 0 0 0 1 0  2 1 0 0 0 0 0
....o...5....o...     | *  *  * * 5  *  * * | 0  0 0 0  0 0  0  2  0  2 0  0 0 0  0 0 | 0 0 0 0 0 1  2 0 1 0 0 0 0
.....o..5.....o..     | *  *  * * * 10  * * | 0  0 0 0  0 0  0  0  1  1 1  1 0 0  0 0 | 0 0 0 0 0 0  1 1 1 1 0 0 0
......o.5......o.     | *  *  * * *  * 10 * | 0  0 0 0  0 0  0  0  0  0 0  1 1 1  1 0 | 0 0 0 0 0 0  0 0 1 1 1 1 0
.......o5.......o     | *  *  * * *  *  * 5 | 0  0 0 0  0 0  0  0  0  0 0  0 0 0  2 2 | 0 0 0 0 0 0  0 0 0 0 2 1 1
----------------------+---------------------+-----------------------------------------+---------------------------
........ x.......     | 2  0  0 0 0  0  0 0 | 5  * * *  * *  *  *  *  * *  * * *  * * | 1 0 1 0 0 0  0 0 0 0 0 0 0
oo......5oo......&#x  | 1  1  0 0 0  0  0 0 | * 10 * *  * *  *  *  *  * *  * * *  * * | 0 1 1 0 0 0  0 0 0 0 0 0 0
.x...... ........     | 0  2  0 0 0  0  0 0 | *  * 5 *  * *  *  *  *  * *  * * *  * * | 0 1 0 1 0 0  0 0 0 0 0 0 0
........ .x......     | 0  2  0 0 0  0  0 0 | *  * * 5  * *  *  *  *  * *  * * *  * * | 0 0 1 0 1 0  0 0 0 0 0 0 0
.oo.....5.oo.....&#x  | 0  1  1 0 0  0  0 0 | *  * * * 10 *  *  *  *  * *  * * *  * * | 0 0 0 1 1 0  0 0 0 0 0 0 0
..x..... ........     | 0  0  2 0 0  0  0 0 | *  * * *  * 5  *  *  *  * *  * * *  * * | 0 0 0 1 0 1  0 0 0 0 0 0 0
..oo....5..oo....&#x  | 0  0  1 1 0  0  0 0 | *  * * *  * * 10  *  *  * *  * * *  * * | 0 0 0 0 1 0  1 0 0 0 0 0 0
..o.o...5..o.o...&#x  | 0  0  1 0 1  0  0 0 | *  * * *  * *  * 10  *  * *  * * *  * * | 0 0 0 0 0 1  1 0 0 0 0 0 0
...o.o..5...o.o..&#x  | 0  0  0 1 0  1  0 0 | *  * * *  * *  *  * 10  * *  * * *  * * | 0 0 0 0 0 0  1 1 0 0 0 0 0
....oo..5....oo..&#x  | 0  0  0 0 1  1  0 0 | *  * * *  * *  *  *  * 10 *  * * *  * * | 0 0 0 0 0 0  1 0 1 0 0 0 0
........ .....x..     | 0  0  0 0 0  2  0 0 | *  * * *  * *  *  *  *  * 5  * * *  * * | 0 0 0 0 0 0  0 1 0 1 0 0 0
.....oo.5.....oo.&#x  | 0  0  0 0 0  1  1 0 | *  * * *  * *  *  *  *  * * 10 * *  * * | 0 0 0 0 0 0  0 0 1 1 0 0 0
......x. ........     | 0  0  0 0 0  0  2 0 | *  * * *  * *  *  *  *  * *  * 5 *  * * | 0 0 0 0 0 0  0 0 1 0 1 0 0
........ ......x.     | 0  0  0 0 0  0  2 0 | *  * * *  * *  *  *  *  * *  * * 5  * * | 0 0 0 0 0 0  0 0 0 1 0 1 0
......oo5......oo&#x  | 0  0  0 0 0  0  1 1 | *  * * *  * *  *  *  *  * *  * * * 10 * | 0 0 0 0 0 0  0 0 0 0 1 1 0
.......x ........     | 0  0  0 0 0  0  0 2 | *  * * *  * *  *  *  *  * *  * * *  * 5 | 0 0 0 0 0 0  0 0 0 0 1 0 1
----------------------+---------------------+-----------------------------------------+---------------------------
o.......5x.......     | 5  0  0 0 0  0  0 0 | 5  0 0 0  0 0  0  0  0  0 0  0 0 0  0 0 | 1 * * * * *  * * * * * * *
ox...... ........&#x  | 1  2  0 0 0  0  0 0 | 0  2 1 0  0 0  0  0  0  0 0  0 0 0  0 0 | * 5 * * * *  * * * * * * *
........ xx......&#x  | 2  2  0 0 0  0  0 0 | 1  2 0 1  0 0  0  0  0  0 0  0 0 0  0 0 | * * 5 * * *  * * * * * * *
.xx..... ........&#x  | 0  2  2 0 0  0  0 0 | 0  0 1 0  2 1  0  0  0  0 0  0 0 0  0 0 | * * * 5 * *  * * * * * * *
........ .xfo....&#xt | 0  2  2 1 0  0  0 0 | 0  0 0 1  2 0  2  0  0  0 0  0 0 0  0 0 | * * * * 5 *  * * * * * * *
..x.o... ........&#x  | 0  0  2 0 1  0  0 0 | 0  0 0 0  0 1  0  2  0  0 0  0 0 0  0 0 | * * * * * 5  * * * * * * *
..oooo..5..oooo..&#xr | 0  0  1 1 1  1  0 0 | 0  0 0 0  0 0  1  1  1  1 0  0 0 0  0 0 | * * * * * * 10 * * * * * *  cycle(BCED)
........ ...o.x..&#x  | 0  0  0 1 0  2  0 0 | 0  0 0 0  0 0  0  0  2  0 1  0 0 0  0 0 | * * * * * *  * 5 * * * * *
....ofx. ........&#xt | 0  0  0 0 1  2  2 0 | 0  0 0 0  0 0  0  0  0  2 0  2 1 0  0 0 | * * * * * *  * * 5 * * * *
........ .....xx.&#x  | 0  0  0 0 0  2  2 0 | 0  0 0 0  0 0  0  0  0  0 1  2 0 1  0 0 | * * * * * *  * * * 5 * * *
......xx ........&#x  | 0  0  0 0 0  0  2 2 | 0  0 0 0  0 0  0  0  0  0 0  0 1 0  2 1 | * * * * * *  * * * * 5 * *
........ ......xo&#x  | 0  0  0 0 0  0  2 1 | 0  0 0 0  0 0  0  0  0  0 0  0 0 1  2 0 | * * * * * *  * * * * * 5 *
.......x5.......o     | 0  0  0 0 0  0  0 5 | 0  0 0 0  0 0  0  0  0  0 0  0 0 0  0 5 | * * * * * *  * * * * * * 1

or
o.......5o.......     & | 10  *  *  * |  2  2  0  0  0  0  0  0 | 1  1  2  0  0  0  0
.o......5.o......     & |  * 20  *  * |  0  1  1  1  1  0  0  0 | 0  1  1  1  1  0  0
..o.....5..o.....     & |  *  * 20  * |  0  0  0  0  1  1  1  1 | 0  0  0  1  1  1  1
...o....5...o....     & |  *  *  * 10 |  0  0  0  0  0  0  2  2 | 0  0  0  0  1  1  2
------------------------+-------------+-------------------------+--------------------
........ x.......     & |  2  0  0  0 | 10  *  *  *  *  *  *  * | 1  0  1  0  0  0  0
oo......5oo......&#x  & |  1  1  0  0 |  * 20  *  *  *  *  *  * | 0  1  1  0  0  0  0
.x...... ........     & |  0  2  0  0 |  *  * 10  *  *  *  *  * | 0  1  0  1  0  0  0
........ .x......     & |  0  2  0  0 |  *  *  * 10  *  *  *  * | 0  0  1  0  1  0  0
.oo.....5.oo.....&#x  & |  0  1  1  0 |  *  *  *  * 20  *  *  * | 0  0  0  1  1  0  0
..x..... ........     & |  0  0  2  0 |  *  *  *  *  * 10  *  * | 0  0  0  1  0  1  0
..oo....5..oo....&#x  & |  0  0  1  1 |  *  *  *  *  *  * 20  * | 0  0  0  0  1  0  1
..o.o...5..o.o...&#x  & |  0  0  1  1 |  *  *  *  *  *  *  * 20 | 0  0  0  0  0  1  1
------------------------+-------------+-------------------------+--------------------
o.......5x.......     & |  5  0  0  0 |  5  0  0  0  0  0  0  0 | 2  *  *  *  *  *  *
ox...... ........&#x  & |  1  2  0  0 |  0  2  1  0  0  0  0  0 | * 10  *  *  *  *  *
........ xx......&#x  & |  2  2  0  0 |  1  2  0  1  0  0  0  0 | *  * 10  *  *  *  *
.xx..... ........&#x  & |  0  2  2  0 |  0  0  1  0  2  1  0  0 | *  *  * 10  *  *  *
........ .xfo....&#xt & |  0  2  2  1 |  0  0  0  1  2  0  2  0 | *  *  *  * 10  *  *
..x.o... ........&#x  & |  0  0  2  1 |  0  0  0  0  0  1  0  2 | *  *  *  *  * 10  *
..oooo..5..oooo..&#xr   |  0  0  2  2 |  0  0  0  0  0  0  2  2 | *  *  *  *  *  * 10  cycle(BCED)

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