29. Viral capsids are made up of morphological subunits called capsomeres. One of the common capsomeres is icosahedral. The icosahedron is a regular polyhedron with
(A) 16 triangular facets and 12 vertices.
(B) 20 triangular facets and 12 vertices.
(C) 16 triangular facets and 16 vertices.
(D) 20 triangular facets and 16 vertices.
Icosahedral Viral Capsids: Structure, Capsomeres, and Geometry Explained
Introduction
Viruses are acellular infectious agents that depend entirely on host cells for replication. Every virus contains genetic material enclosed within a protective protein shell called the capsid. This capsid protects the viral nucleic acid from physical damage, enzymatic degradation, and environmental stress while also helping the virus recognize, attach to, and enter host cells. The capsid itself is composed of repeating protein subunits known as capsomeres, which assemble into highly symmetrical structures.
One of the most common and evolutionarily successful capsid architectures is the icosahedral symmetry. An icosahedron is a highly symmetrical geometric solid that provides maximum internal volume while using the minimum number of structural proteins. This arrangement allows viruses to package their genomes efficiently with remarkable structural stability. Many medically important viruses, including adenovirus, poliovirus, rhinovirus, papillomavirus, and numerous bacteriophages, possess icosahedral capsids.
Correct Answer
Correct Option: (B) 20 triangular facets and 12 vertices
Detailed Explanation
An icosahedron is one of the five Platonic solids and represents the most efficient three-dimensional geometric structure for constructing a closed viral capsid. It consists of exactly 20 equilateral triangular faces (facets), 12 vertices, and 30 edges. Each triangular face is formed by tightly packed capsomeres, while five triangular faces meet at every vertex, producing an exceptionally stable and symmetrical structure.
The remarkable advantage of icosahedral symmetry is that a virus can build a large protective shell by repeatedly using identical protein subunits instead of synthesizing numerous different proteins. This minimizes genetic requirements while maximizing structural stability. Consequently, many DNA and RNA viruses have adopted icosahedral symmetry during evolution.
The viral capsid itself is not composed of a single protein but rather multiple copies of one or a few capsid proteins arranged into capsomeres. Depending on the complexity of the virus, the number of capsomeres may vary according to the triangulation number (T number), but the fundamental geometric shape always remains an icosahedron with 20 triangular faces and 12 vertices.
Explanation of Each Option
Option (A): 16 Triangular Facets and 12 Vertices
This statement is incorrect. An icosahedron always possesses 20 triangular faces. Sixteen triangular facets do not correspond to any regular icosahedral geometry.
Option (B): 20 Triangular Facets and 12 Vertices
This statement is correct. A regular icosahedron contains exactly 20 equilateral triangular faces, 12 vertices, and 30 edges, making it the most common capsid architecture in viruses.
Option (C): 16 Triangular Facets and 16 Vertices
This statement is incorrect. Neither the number of triangular faces nor the number of vertices matches the geometry of a regular icosahedron.
Option (D): 20 Triangular Facets and 16 Vertices
This statement is incorrect. Although the number of triangular faces is correct, an icosahedron has only 12 vertices, not 16.
Why Option (B) is Correct
An icosahedron is defined geometrically as a regular polyhedron having 20 equilateral triangular faces, 12 vertices, and 30 edges. Viral capsids with icosahedral symmetry follow this exact geometric arrangement.
Why the Other Options are Incorrect
Why Option (A) is Incorrect
An icosahedron cannot possess only 16 triangular facets because its defining characteristic is the presence of 20 triangular faces.
Why Option (C) is Incorrect
The values for both facets and vertices are incorrect and do not describe any regular icosahedron.
Why Option (D) is Incorrect
Although 20 triangular facets are correct, an icosahedron always contains 12 vertices rather than 16.
Comparison of All Options
| Option | Triangular Facets | Vertices | Status |
|---|---|---|---|
| A | 16 | 12 | Incorrect |
| B | 20 | 12 | Correct |
| C | 16 | 16 | Incorrect |
| D | 20 | 16 | Incorrect |
Geometry of an Icosahedral Capsid
| Property | Value |
|---|---|
| Triangular Faces (Facets) | 20 |
| Vertices | 12 |
| Edges | 30 |
| Faces Meeting at Each Vertex | 5 |
| Symmetry | Icosahedral |
Examples of Icosahedral Viruses
| Virus | Genome | Capsid Symmetry |
|---|---|---|
| Adenovirus | Double-stranded DNA | Icosahedral |
| Poliovirus | Positive-sense RNA | Icosahedral |
| Rhinovirus | Positive-sense RNA | Icosahedral |
| Papillomavirus | Double-stranded DNA | Icosahedral |
| Norovirus | Positive-sense RNA | Icosahedral |
Comparison of Major Viral Symmetries
| Symmetry | Shape | Examples |
|---|---|---|
| Icosahedral | Spherical/polyhedral | Adenovirus, Poliovirus |
| Helical | Rod-shaped | Tobacco mosaic virus, Rabies virus |
| Complex | Neither purely helical nor icosahedral | Bacteriophages, Poxviruses |
Biological Significance
Icosahedral symmetry enables viruses to construct highly stable protective shells using repeated copies of identical protein subunits. This minimizes the amount of genetic information required to encode structural proteins while maximizing capsid strength and internal storage capacity. Such efficient design has contributed to the evolutionary success of numerous viral families infecting humans, animals, plants, and bacteria.
Final Answer
Correct Option: (B)
A regular icosahedron consists of 20 equilateral triangular facets (faces), 12 vertices, and 30 edges. This highly symmetrical geometry is one of the most common capsid architectures found in viruses.
