srid

Acronym srid

TOCID symbol rID

Name small rhombicosidodecahedron,
expanded icosahedron,
expanded dodecahedron

 © ©    ©

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

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 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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