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694:{\displaystyle (0,0,1),\left({\frac {{\sqrt {5}}-1}{2}},1,{\frac {{\sqrt {5}}-1}{2}}\right),\left({\frac {{\sqrt {5}}-1}{2}},{\frac {{\sqrt {5}}+1}{2}}\right).}
317:
1541:
1536:
968:
Adventures Among the
Toroids: A Study of Quasi-Convex, Aplanar, Tunneled Orientable Polyhedra of Positive Genus Having Regular Faces With Disjoint Interiors
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241:, meaning a figure featuring two triangles adjacent to opposite sides of a square. Therefore, the faces of a bilunabirotunda possess 8
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416:{\displaystyle \left(2+2{\sqrt {3}}+{\sqrt {5(5+2{\sqrt {5}})}}\right)a^{2}\approx 12.346a^{2},}
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98:
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909:
Timofeenko, A. V. (2009). "The Non-Platonic and Non-Archimedean
Noncomposite Polyhedra".
296:, meaning that it cannot be separated by a plane into two small regular-faced polyhedra.
701:
under the group's action (of order 8) generated by reflections about coordinate planes.
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28:
712:
discusses the bilunabirotunda as a shape that could be used in architecture.
1014:
229:
with faces of 8 equilateral triangles, 2 squares, and 4 regular pentagons.
218:
91:
81:
722:
Regular_dodecahedron § Space_filling_with_cube_and_bilunabirotunda
487:{\displaystyle {\frac {17+9{\sqrt {5}}}{12}}a^{3}\approx 3.0937a^{3}.}
246:
1023:
Miracle
Spacefilling (Dodecahedron&Cube&Johnson solid No.91)
791:
Animation of tessellation of cubes, dodecahedra and bilunabirotunda
777:
206:
1027:
1031:
753:
726:
Six bilunabirotundae can be augmented around a cube with
501:
One way to construct a bilunabirotunda with edge length
299:
The surface area of a bilunabirotunda with edge length
820:
Berman, M. (1971). "Regular-faced convex polyhedra".
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144:
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97:
74:
35:
21:
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523:
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415:
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164:
936:Reynolds, M. A. (2004). "The Bilunabirotunda".
1043:
237:The bilunabirotunda is named from the prefix
8:
1542:metagyrate diminished rhombicosidodecahedron
1537:paragyrate diminished rhombicosidodecahedron
734:labeled this six-bilunabirotunda model as 6J
165:{\displaystyle \mathrm {D} _{2\mathrm {h} }}
1562:gyrate bidiminished rhombicosidodecahedron
1547:bigyrate diminished rhombicosidodecahedron
1050:
1036:
1028:
795:12 bilunabirotundae around a dodecahedron
197:
27:
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261:polyhedron in which all of the faces are
155:
151:
146:
143:
815:
813:
811:
748:
709:
423:and the volume of a bilunabirotunda is:
265:—enumerated as 91st Johnson solid
1557:metabidiminished rhombicosidodecahedron
1552:parabidiminished rhombicosidodecahedron
1310:elongated pentagonal orthocupolarotunda
807:
1502:metabiaugmented truncated dodecahedron
1497:parabiaugmented truncated dodecahedron
1345:gyroelongated pentagonal cupolarotunda
1315:elongated pentagonal gyrocupolarotunda
742:). Such clusters combine with regular
18:
857:"Johnson solids & their acronyms"
7:
1567:tridiminished rhombicosidodecahedron
746:to form a space-filling honeycomb.
1522:metabigyrate rhombicosidodecahedron
1517:parabigyrate rhombicosidodecahedron
1507:triaugmented truncated dodecahedron
1458:augmented tridiminished icosahedron
1320:elongated pentagonal orthobirotunda
979:, (page 127, 2nd ed.) polyhedron 6J
1350:gyroelongated pentagonal birotunda
1325:elongated pentagonal gyrobirotunda
1300:elongated pentagonal orthobicupola
1285:elongated triangular orthobicupola
156:
147:
14:
1532:diminished rhombicosidodecahedron
1340:gyroelongated pentagonal bicupola
1330:gyroelongated triangular bicupola
1305:elongated pentagonal gyrobicupola
1290:elongated triangular gyrobicupola
822:Journal of the Franklin Institute
774:6 bilunabirotundae around a cube
531:is by union of the orbits of the
1527:trigyrate rhombicosidodecahedron
1492:augmented truncated dodecahedron
1235:gyroelongated pentagonal rotunda
1147:gyroelongated pentagonal pyramid
911:Journal of Mathematical Sciences
768:
759:
752:
716:Related polyhedra and honeycombs
1477:augmented truncated tetrahedron
1404:metabiaugmented hexagonal prism
1399:parabiaugmented hexagonal prism
1230:gyroelongated pentagonal cupola
1220:gyroelongated triangular cupola
1177:gyroelongated square bipyramid
1172:elongated pentagonal bipyramid
1162:elongated triangular bipyramid
559:
541:
374:
355:
253:as it faces. It is one of the
1:
1512:gyrate rhombicosidodecahedron
1379:triaugmented triangular prism
1335:gyroelongated square bicupola
1295:elongated square gyrobicupola
1270:pentagonal orthocupolarotunda
524:{\displaystyle {\sqrt {5}}-1}
213:3D model of a bilunabirotunda
16:91st Johnson solid (14 faces)
1626:triangular hebesphenorotunda
1448:metabidiminished icosahedron
1438:metabiaugmented dodecahedron
1433:parabiaugmented dodecahedron
1409:triaugmented hexagonal prism
1389:biaugmented pentagonal prism
1374:biaugmented triangular prism
1275:pentagonal gyrocupolarotunda
1215:elongated pentagonal rotunda
1142:gyroelongated square pyramid
1137:elongated pentagonal pyramid
1127:elongated triangular pyramid
834:10.1016/0016-0032(71)90071-8
1225:gyroelongated square cupola
1210:elongated pentagonal cupola
1200:elongated triangular cupola
888:. p. 86–87, 89.
855:Francis, D. (August 2013).
1679:
1487:biaugmented truncated cube
1384:augmented pentagonal prism
1369:augmented triangular prism
1167:elongated square bipyramid
886:Cambridge University Press
719:
1634:
1453:tridiminished icosahedron
1443:triaugmented dodecahedron
1394:augmented hexagonal prism
1280:pentagonal orthobirotunda
950:10.1007/s00004-004-0005-8
923:10.1007/s10958-009-9655-0
196:
26:
1482:augmented truncated cube
1260:pentagonal orthobicupola
1245:triangular orthobicupola
1132:elongated square pyramid
878:Cromwell, P. R. (1997).
1265:pentagonal gyrobicupola
1205:elongated square cupola
765:Spacefilling honeycomb
1638:List of Johnson solids
1601:augmented sphenocorona
1428:augmented dodecahedron
792:
695:
525:
488:
417:
313:
286:
285:{\displaystyle J_{91}}
214:
166:
1658:Elementary polyhedron
1591:snub square antiprism
938:Nexus Network Journal
790:
728:pyritohedral symmetry
720:Further information:
696:
526:
497:Cartesian coordinates
489:
418:
314:
294:elementary polyhedron
292:. It is known as the
287:
243:equilateral triangles
212:
167:
1611:hebesphenomegacorona
1250:square orthobicupola
1157:pentagonal bipyramid
1152:triangular bipyramid
538:
505:
427:
323:
303:
269:
142:
119:Vertex configuration
1640:, a sortable table)
1255:square gyrobicupola
1469:Archimedean solids
1108:pentagonal rotunda
1088:pentagonal pyramid
1002:Weisstein, Eric W.
793:
691:
521:
484:
413:
309:
282:
215:
162:
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1578:elementary solids
1103:pentagonal cupola
1093:triangular cupola
895:978-0-521-66405-9
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312:{\displaystyle a}
251:regular pentagons
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1616:disphenocingulum
1606:sphenomegacorona
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1586:snub disphenoid
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1420:Platonic solids
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1240:gyrobifastigium
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1006:Bilunabirotunda
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263:regular polygon
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223:bilunabirotunda
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22:Bilunabirotunda
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1083:square pyramid
1079:
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1059:Johnson solids
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995:External links
993:
990:
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977:978-0686119364
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928:
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1098:square cupola
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1010:Johnson solid
1007:
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725:
708:
705:Applications
500:
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216:
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744:dodecahedra
533:coordinates
126:8(3.4.3.5)
1652:Categories
1636:(See also
1359:Augmented
802:References
233:Properties
184:elementary
176:Properties
128:2(3.5.3.5)
1467:Modified
1418:Modified
1186:Modified
1117:Modified
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881:Polyhedra
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861:Word Ways
647:−
612:−
581:−
516:−
466:≈
395:≈
257:—a
92:pentagons
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1192:rotundae
1119:pyramids
1075:rotundae
1067:Pyramids
249:, and 4
219:geometry
109:Vertices
1188:cupolae
1071:cupolae
971:(1980)
842:0290245
247:squares
124:4(3.5)
87:squares
40:Johnson
1576:Other
1361:prisms
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